Math Practice G Standard

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LEVEL G

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Level G Chapter 1

In Chapter 1, we will expand on

Integer Operations

Understanding integers is important because they are the foundation of our number system.

• We will plot and compare positive and negative numbers and use them in real-world situations.

• We will find absolute values and opposite numbers.

• We will model ways to add and subtract integers.

• We will model ways to multiply and divide integers.

• We will use order of operations to simplify number sentences.

Circle the number that best represents each situation.

The submarine traveled 3,000 feet below sea level.

2. You paid $20 to buy a book.

3. The town’s population increased by 4,560.

4. It was 23 degrees below zero outside.

5. The car drove at 35 miles per hour.

Write >, <, or = to compare the integers.

62

Order given values from least to greatest and then plot the numbers on the number line.

Use the information provided to fill-in the table.

Anne, Sarah, Beth, and Eliza all compared their bank accounts. Anne has the least amount of money and Beth had the most. Sarah had a negative balance in her account. The amount in the accounts were $460, -$10, $250 and -$112.

The temperatures in four cities were recorded on a particularly cold day. City A had a temperature below freezing. City B had a temperature slightly above freezing. City C had the coldest temperature. City D had the highest temperature. The recorded temperatures were -20°C, 2°C, 35°C, and -10°C, where 0°C is considered freezing.

Find the opposite and absolute value of each integer.

Determine the absolute value of the number indicated on the number line.

Order the following from least to greatest.

A diver starts at the surface of the ocean which is 0 m above sea level. He dove 20 meters and then turned around to swim back to the surface of the ocean.

What is the total distance the diver swam?

Jack takes an elevator from the 9th floor of his building to the third level of the parking lot below the building. How many total floors did he travel?

The temperature was 15 degrees in the morning and then dropped to negative 3 degrees by the evening.

What was the total change in temperature?

Emily owes her friend $15 and then borrows another $12 from the same friend.

How much does Emily owe her friend in total?

Lesson instructions

Use number lines or counters to model adding integers.

Write and solve the addition equation represented by the number line.

Write an expression and solve.

Use the number line to solve.

Nelly opened a lemonade stand. She borrowed $5 to pay for supplies. She then made $13 selling lemonade. How much money does she make in the end?

Corey runs up 7 rows of steps in a stadium and then down 11 rows. How many rows must he run back up to return to his starting point?

Hint: use 0 as his starting point

Use counters to solve.

A diver descends 8 feet below the surface and then ascends 4 feet. What depth is he at now?

dollars feet rows degrees

The temperature at 7 AM was -5 degrees. By 10 AM it warmed up 2 more degrees. What was the temperature at 10 AM?

Add the integers. Same Sign Add:

+ 5 = 8

+ -5 = - 8 Different Sign Subtract:

+ 5 = 2

+ -5 = -2

Answer has the same sign. Answer takes the sign of the number with the greater absolute value.

Evan’s thermometer is broken. It currently reads -18 degrees. The actual temperature is 6 degrees higher. What is the current temperature?

Anna had a balance in her bank account of -$15. Then she was paid $18 for babysitting. What is the new balance of her bank account?

A diver was 12 meters below sea level and then swam up 7 meters. How far from the surface is the diver?

George lost 9 points on a test. His teacher gave him 8 points for correcting his mistakes and an additional 3 points for completing the challenge question. After these adjustments, how many more points will George have compared to his original score?

meters points

Lesson instructions

Use number lines or counters to model subtracting integers.

Use the number line to solve.

Use the number line to solve.

A hiker begins at base camp and travels 5 kilometers up a mountain. She then hikes 8 kilometers down the mountain into the valley. How far is she from the base camp?

Frank has $80 in his bank account. He spends $110 at the autobody shop. What is the balance of his bank account now?

Use counters to solve.

The inside of a cooler was 3 degrees below freezing. After adding ice to the cooler, the temperature dropped by 5 degrees. Then the cooler was placed outside where the temperature decreased another 4 degrees. What was the final temperature inside the cooler?

degrees

Judy was playing a game and had a score of 3. She lost 6 points and then lost another 4. How many points did she have at the end?

Subtract the two integers.

Subtract the three integers. 1. 2 − 6 =

7 − (-8) =

3 − 2 − 7 = 13. 7 − 5 −(-6) = 15. 4 − (-6) − 2 = 17. -5 − 6 − (-5) = 19. -9 − (-2) − (-8) = 2. 4 − 9 =

-4 − 5 =

-8 − (-6) =

-7 − (-7) =

6 − (-4) = 6. -3 − 9 = 8. -9 − (-5) = 10. -3 − (-9) = 12. 6 − 8 − 9 = 14. 9 − (-3) − (-4) = 16. -8 − (-1) − 3 = 18. -3 − (-2) − 7 = 20. 8 − (-9) − 5 =

Helen was asked to solve the problem -9 − 7. She completed the following steps to solve:

Step 1: Rewrite → -9 − 7 = -9 + 7

Step 2: Add → -9 + 7 = -2

Circle the step where she made an error and then explain how to solve from there.

Kayla was asked to solve the problem 5 − (-3) − 6. She completed the following steps to solve:

Step 1: Solve → 5 − (-3) = 5 − 3 = 2

Step 2: Solve → 2 − 6 = 2 + -6 = -4

Circle the step where she made an error and then explain how to solve from there.

Donna and Judy were asked to solve the subtraction problem -6 − (-4). Donna stated the answer was -10 and Judy said the answer was -2. Who was correct?

Rachel and Ann were asked to solve the subtraction problem 7 − (-5) − 9. Rachel said the answer was 3, but Ann said the answer was -11. Who was correct?

instructions

Multiply the integers.

Complete the chart.

2 × 3

-8 × 9

-2 × -2

6 × -3 × 2

-7 × 5 × -9

Determine if each statement is true or false. Correct the false statements.

As a train comes to a stop, it needs to decrease its speed. The conductor records decreases to the train’s speed as negative numbers.

The train decreased its speed by 5 miles per hour every minute.

• What was the total change in speed after 7 minutes?

miles per hour

• What was the total change in speed after 9 minutes?

miles per hour

A pet store keeps track of the number of fish they have in stock. They use negative numbers when they sell fish and positive numbers when they buy more fish.

They sold 3 fish every hour for the first 5 hours of the day. Write an expression to represent the change in the number of fish during the first 5 hours of the day and solve.

A diver keeps track of his changes in depth as he swims. He uses positive numbers for when he comes up and negative numbers for when he goes down.

To explore the ocean floor, he needs to descend 6 feet every minute.

• What was the total change in depth after 5 minutes? feet

• What was the total change in depth after 8 minutes?

feet

A bookstore uses negative numbers to represent book sales and positive numbers to represent restocking.

The store sold 4 books every hour for the first 6 hours of the day. Write an expression to represent the change in the number of books during the first 6 hours of the day and solve.

Complete the chart.

Points lost are scored as negative numbers. Points gained are scored as positive numbers.

Sara plays 4 rounds of a game. Her score is -12 and she lost the same amount of points in each round. How many points did she lose in each round?

A pilot tracks changes in the plane’s height. He uses positive numbers to represent rising and negative numbers to represent landing.

The plane descended 600 feet over 15 minutes. What is the rate of descent per minute, expressed as an integer?

feet per minute points

Sam’s bank uses positive numbers to show deposits and negative numbers to show charges.

Sam signs up for a 30-day meal subscription that costs $180 in total. If the same fee is charged daily to his bank account, what is the daily change to his bank account?

A florist records flower sales as negative numbers.

The florist started the week with a stock of 175 flowers. By the end of the week, the florist had sold all the flowers and had none left. On average, what was the change in the number of flowers each day?

instructions

Solve the word problems involving integer operations.

Positive Changes

increase, gain, deposit (put in), ascend (climb), earn, receive, rise, save

• She received $10 → +$10

• Temperature rose 4 degrees

• He deposited $50 → +$50

Match the word problem to the correct operation.

Negative Changes

decrease, lose, withdraw (take out), descend (climb down), spend, give away, drop, owe

• He withdrew $55

• Temperature dropped 7 degrees

• She owes her friend $15

1. Amy’s bank account has -$16. She deposits $25. What is her new balance?

2. The average temperature last month was -16 degrees. The average temperature this month is 25 degrees. What is the difference in average temperature between this month and last?

3. A product costs a company $16 to make. What is the change to their bank account when they make 25 of the product?

4. A hiker takes 16 minutes to descend 25 meters. What is the hiker’s change in elevation per minute?

Solve the word problem. Use a positive or negative integer to represent change.

5. During the day, the temperature in a city was 9 degrees below zero. By the afternoon, the temperature had increased 4 degrees. What was the temperature in the afternoon?

6. A company’s profit dropped by the same amount each month for 6 months. If the total loss over that time was $42,000, what was the change in profit per month?

7. Dennis drove 35 miles from his house to visit a friend. On his way home, he stopped for gas after driving 16 miles. How far away is he from his house?

8. A diver descends 12 feet every minute. What would be the diver’s total change in depth after 5 minutes?

In a game, players start with zero points. In order to win, they need 15 points. If Sarah has -8 points, how many more points does she need to win?

John has $15 taken out of his bank account each day he uses his rental car. If John rents the car for 6 days, what is the change in his bank account written as integer?

The temperature drops 2 degrees every hour. What would be the total change in temperature after 8 hours written as an integer?

A freezer’s temperature started at -20 degrees. After an hour, the temperature rose 3 degrees. After another hour, the temperature dropped 8 degrees. What is the freezer’s final temperature?

Lesson instructions

Simplify.

(3)2 =

(7)2 =

(-10)3 =

(-6)2 =

(-4)2 =

(5)3 =

Use PEMDAS and the order of operations to solve. Parentheses Exponents Multiplication Division Addition Subtraction

From Left to Right From Left to Right

Solve using order of operations.

19. -42 + 18 ÷ 6 = 21. (7 − 9) + (-5)2 =

23. 14 − (6 + 4) ÷ -5 = 25. 8 + (3 − 6) ÷ 3 − 5 = 27. -45 ÷ 9 × 3 + (3 − 5)2 =

-(2)2 =

(10)2 =

(-5)2 =

(4)3 =

(12)3 =

(6)3 =

(4)2 =

(-9)3 =

(-8)3 =

(-2)3 =

(-3)2 =

-(9)2 = 20. -15 ÷ 3 + -4 = 22. 6 × (-4 + 3) = 24. (5 − 8) + 32 × -7 = 26. 4 3 − (8 ÷ 2) + 7 × 3 = 28. -72 + 8 × 3 − (5 − 8)3 =

A submarine is hovering at 150 feet below sea level.

The captain orders a dive, descending 20 feet per minute for 6 minutes.

They spot a shark above them and ascend (go up) 80 feet.

Then they follow the shark down another 40 feet.

What is the submarine’s final depth?

A chemical in a lab is sitting at room temperature, 20°C.

The scientist places it in a freezer, causing the temperature to drop by 4°C per minute for 8 minutes.

She then takes it out and places it on a heater, raising the temperature by 15°C.

Finally, she adds a cooling agent that instantly drops the temperature by 10°C. What is the final temperature of the solution?

A hiker starts at a base camp located at an altitude of 500 feet. He descends into a valley, ending at an altitude of -100 feet.

This descent took him exactly 4 hours.

How many feet did he descend per hour?

Mr. Smith buys a stock worth $50.

For the next 4 days, the stock price drops by $3 each day.

The next day, the company announces bad news, and the remaining price is cut in half (divided by 2).

The following day, the price recovers slightly, going up by $2.

What is the final price of the stock?

Solve.

Addition:

3 + 2 = 5

-3 + 2 = -1

3 + (-2) = 1

-3 + -2 = -5

Subtraction:

3 - 2 = 1

-3 − 2 = -5

-3 - (-2) = -1

3 - (-2) = 5

Solve.

Multiplication:

3 × 2 = 6

-3 × -2 = 6

3 × -2 = -6 -3 × 2 = -6

Division:

6 ÷ 2 = 3

-6 ÷ -2 = 3

-6 ÷ 2 = -3

6 ÷ -2 = -3

Solve.

4² + (3 - 8) × -7 + (-3)

P: 4² + -5 × -7 + (-3)

E: 16 + -5 × -7 + (-3)

M/D: 16 + 35 + (-3)

A/S: 48

20 + -7 = 3. -23 + -19 =

-38 − 24 =

-98 − (-45) =

445 − (-56) =

-77 + 30 =

33 + -57 =

-3 − 35 =

47 − (-41) =

808 + -367 =

4 × -9 =

-46 × -3 =

-78 × -8 =

-288 ÷ -12 =

-4,000 ÷ 5 =

-7 × 5 =

20 × -16 =

-105 ÷ 7 =

475 ÷ -25 =

-2,400 ÷ -8 =

32 + 4 × 2 =

14 + 3 − (36 ÷ 3) =

(18 − 23) × 72 − (-45) =

64 ÷ 25 × (-26 + 45) + -48 =

-6 + (8 − 3)2=

62 ÷ -4 + (11 × 6) =

45 + 7 − (-19 + 33) =

95 − 45 ÷ (62 − 31) − (-10) =

A car begins to travel on a road at an altitude of 30 feet. The road slopes down and the car stops at an altitude of -15 feet. How many feet did the car descend?

Fill in the table based on the word problem.

Arnold started out with -$42 in his bank account and has 4 bills to pay with the following values: $56, $24, $18, and $34. He worked 16 hours and makes $25 per hour. How much will he have after paying bills and getting paid?

Description Amount

Starting Amount

Bill #1

Bill #2

Bill #3

Bill #4

Pay

Final Amount

At 4:00 AM the temperature is -8 degrees Fahrenheit. By 9:00 AM the temperature warmed up by 17 degrees. What is the temperature at 9:00 AM?

Rebecca is tracking her business expenses and profits for her store. She started the week with -90 dollars in her business account. She spends $45 per day on shipping costs for 7 days. She also earns $15 profit per order, and she had 10 orders.

Description Amount

Starting Amount

Shipping Costs

Total Profit

Final Amount

Chapter 2

In Chapter 2, we will expand on

Operations with Rational Numbers

It is important to be able to work fluently with fractions and decimals.

• We will convert fractions to decimals and decimals to fractions.

• We will compare fractions and decimals.

• We will practice adding, subtracting, multiplying, and dividing fractions and decimals in real-world situations.

• We will apply order of operations to numbers sentences with fractions and decimals.

Circle the equivalent decimal.

Fill in the table. Write yes or not to show if the decimal repeats.

Megan has 4 5 9 ounces of juice in her bottle. Convert this value to a decimal.

A piece of wood needs to be cut into 9 equal pieces. If the piece of wood is 7 feet long, how long is each piece?

Tickets to a state fair are on sale 3 for $100. What is the cost of 1 ticket during this sale?

Eli is painting his house and each gallon of paint can cover 110 square feet. If Eli needs to paint 900 square feet, how many gallons of paint does he need?

Express your answer as a decimal.

Lesson instructions 2

Compare and order rational numbers.

Order the following from least to greatest.

Write >, < or = to compare the numbers.

Place the numbers on the number line.

The depths of four submarines are -84.5, -84 1 5 ,767 9 , and -84.55 meters. Order these depths from deepest to shallowest.

5 hikers are on 5 different trails and their elevation above sea level is as follows: 55 m, 55 1 3 m, 55.5 m, 499 9 m, and 55.55 m. Order these elevations from lowest to highest.

The temperature over four days was -15.2°, -15 1 4 °, - 155 11 °, and -15 3 8 °. Order these temperatures from coldest to warmest.

During a rainy week, the amount of rainfall that fell over four days was recorded as 2.3 inches, 23 9 inches, 2 1 3 inches, and 2.34 inches. Order these rainfall amounts from least to greatest.

Lesson instructions 3 Add or subtract positive and negative decimals.

+ -8.9

Identify the mistake made when solving and re-solve to find the correct answer.

Problem Resolve

1. 5.4 + -3.48 = 8.88

2. -22.32 − 12.45 = 34.77

3. 8.76 − 5.2 = 8.24

4. 8.55 + 1.56 − (-1.99) = 8.12

Solve.

45.6 − 21.34

-19.4 + -23.89

-25.7 + 10.9

-22.32 − 12.45 + 8.3

Which of the following has the largest sum?

67.5 − (-45.312)

-12.8 − (-7.3)

-18.65 − 9.12

8.55 + 1.56 − (-1.99)

4.005 + -2.1

A painter used 12.53 liters, 8.7 liters, and 19.451 liters of paint for three projects. How many liters were used in total?

Jeffrey had $35.50 in his bank account and purchased groceries for $45.20. How much money does Jeffery have in his bank account now?

Donald recorded miles driven towards his destination as positive numbers and miles driven towards home as negative numbers. He drove 56.3 miles one day, -27.81 miles another day, and then -16.501 miles on the third day. How many total away from home was he by the third day?

The temperature was -8.5 degrees in the morning and it dropped 6.25 degrees by the afternoon. What was the temperature in the afternoon?

Lesson instructions 4

Multiply or divide positive and negative decimals.

Solve.

3.5 × -2 =

-2.5 × 6.4 =

-4.33 × -2.5 =

-4.25 × 5.5 =

Solve.

4.50 ÷ -1.50 =

Solve. 31. 9.8 × -1.25 × 5.5 = 33. -0.75 × -2.33 × 7.2 =

Arnold deposited $78.32 to his bank account each day for 4 days. How much did Arnold deposit in total?

If a submarine starts at the surface of the ocean and then travels at a rate of -12.63 meters per hour for 6 hours, what is the depth of the submarine at 6 hours?

The temperature in a freezer begins at 0 degrees and decreases at a constant rate over 5 hours until it reaches -12.35 degrees. What is the change in temperature per hour?

The floor of a pool is 16.2 feet below the ground. As it is being filled, the water level rises by 2.7 feet per hour. How many hours does it take to reach the top?

Lesson instructions 5 Solve each word problem.

+ - × ÷

sum, total, plus, increase by, more than, combined, together difference, minus, decrease by, less than, fewer, left product, times, multiplied by, twice, each, every quotient, divided by, per, ratio, split, share equally

Match the word problem to the correct operation.

1. The temperature dropped to -12.5°C last night. This morning it is 7.3°C. What is the difference in temperature between last night and this morning?

2. A diver’s starting depth is -12.5 meters. He ascends, or swim upwards, 7.3 meters. What is his new depth?

3. A pool loses 12.5 liters of water over 7.3 hours. How many liters of water are lost per hour?

4. Mannie paid $12.50 per pound of chocolate and he bought 7.3 pounds. How much did he need to remove from his bank account to pay for the chocolate?

Choose the expression that helps solve the word problem.

5. Kelly’s bank account has -$35.75. She deposits $45.20. What is her new balance?

7. A water tank loses -4.25 liters of water each day due to a leak. If the leak continues for 12 days, what is the total water loss?

12 ÷ -4.25

-4.25 × 12

-4.25 + 12

6. The temperature last week was -7.5°C. This week, the temperature is 15.8°C. What is the difference in temperature between the two weeks?

15.8 − (-7.5) B. -7.5 + 15.8

15.8 × -7.5

8. A diver descends 18.5 meters in 7.4 minutes. How far does the diver descend per minute? A. 18.5 × 7.4

18.5 − 7.4

-18.5 + 7.4 D. -18.5 ÷ 7.4

Ruth wants to buy a salad for $14.65, a water for $2.45, and a bag of chips for $3.68 for her lunch. If she has a $20 bill, does she have enough money to purchase all three items? Explain.

A swimming pools drains 510.65 liters per hour. If the pool starts at 6,250.85 liters and then drains for 4.83 hours, how much water will be remaining?

Fill in the table and then solve.

A hiker needs to cover a total distance of 42.6 kilometers. He hikes at a consistent rate of 4.75 kilometers per hour. Calculate how much distance he still needs to cover after 1, 2, and 3 hours of hiking.

The temperature drops at a rate of -5.72°C per hour. Calculate the temperature after 2 hours, 4 hours, and 6 hours if the starting temperature is 0°C.

Subtract.

Anna measured 3 4 cup of sugar into a bowl. When she reread the recipe, she realized she needed 1 1 4 cup of sugar. How many cups of sugar does she have to add?

At 1:00pm, Jack ate 3 10 of a candy bar. At 3:00 he ate 5 10 of a candy bar. What fraction of the candy bar did he eat today?

Tom used 2 1 8 gallons of paint for a wall. He used another 3 8 gallon for the closet. How much paint did he use in all?

A water tank was filled with 5 1 4 gallons of water. It leaked 3 4 a gallon of water. How much water was left in the water tank?

Subtract.

7

Howard needs 6 1 4 cups of flour for a recipe. He has 5 3 8 cups of flour. How many additional cups of flour does he need?

Emma's teacher wrote -1 1 2 points on a question on her test. After Emma corrected the problem, her teacher gave her back 3 4 of a point. How many total points did Emma lose on the test?

The total snowfall after a storm was 2 5 6 inches. After three days, the amount of snow on the ground was 7 8 of an inch. How much snow melted in those 3 days?

Moses had to complete 1 1 2 hours of volunteering. He volunteered for 3 8 an hour over the weekend. How much more time does he need to volunteer?

A bucket is leaking water. The water level in the bucket drops - 2 3 of an inch every hour. How much does the water level change in 1 2 of an hour?

A cliff loses - 1 8 of a foot of rock every year due to waves. How much rock is lost in 11 1 2 years?

Sarah's teacher wrote -4 1 2 points on top of her test. She lost 1 2 a point for each spelling error. How many spelling errors did Sarah make?

A diver is at a depth of -12 1 4 meters. If he swam down at a steady pace of -1 3 4 meters per minute, how many minutes has he been diving?

Solve each word problem. + - × ÷

sum, total, plus, increase by, more than, combined, together difference, minus, decrease by, less than, fewer, left

Match the word problem to the correct operation.

product, times, multiplied by, twice, each, every quotient, divided by, per, ratio, split, share equally

1. A submarine is positioned 5 2 3 miles below sea level. If it rises 5 6 of a mile, how far below sea level will it be?

2. The temperature drops 5 6 of a degree every hour. After 5 2 3 hours, what would be the total temperature change?

3. A lake lost a total of 5 6 cubic meters of water during a drought. If the drought lasted 5 2 3 months, what was the change in volume of the lake per month?

4. A biker had 5 2 3 miles in a race to complete. If he already biked 5 6 of a mile, how much further did he have to go?

Choose the operation that best matches the word problem.

5. A stone sinks at a rate of 1 7 8 meters per second. If a lake is 45 meters deep, how long would it take the stone to reach the bottom of the lake?

6. Solomon needed to make 1 1 4 batches of cookies. If he makes 7 8 of a batch one day, how much more does he need to make?

7. A diver descends at a rate of 8 1 5 meters per minute. How many meters deep is he after 12 minutes?

8. Leo started with - 2 5 points in a game. He then gained 1 7 8 point. How many points does he now have?

9

Rose had 6 1 6 feet of ribbon that she cut 8 9 of a foot from. How much ribbon does she have left?

A bucket contains 500 milliliters of water. It has a slow leak that allows water to drip out at a rate of 1 1 4 milliliters every minute. How many minutes will it take for the bucket to be completely empty?

George hikes down a 11 1 5 kilometer hill at a rate of 1 2 5 kilometers per hour. How many hours will it take him to reach the bottom?

Danny missed 8 problems on a math test. For each problem missed, he lost 2 3 of a point. What is the total point change to Danny’s test score due to these missed problems?

Lesson instructions 10

Convert values to either fractions or decimals and use PEMDAS and the order of operations to solve.

From Left to Right

From Left to Right

1. -4.5 + (2.3 × -1.8) − 3.2 3. -2(1.5 + -3.2) − 12.4

5.5 − (-2.8 ÷ 1.4) × 3.6 + (-3)2 7. -2 1 3 + (- 5 6 × 1 10 ) − 1 4

9. (- 3 7 × 7 8 ) − (- 4 3 ) ÷ 2 9

11. 1 5 6 − (- 4 3 ÷ 2 7 ) + 1 2

13. (2.5 × - 3 4 ) × 2 3 − 1.2 15. (-2)3 × (4.2 − 1 5 ) + -2 2 5

(7.5 − -32) ÷ -2 + 3.25

-3.2 + -42 ÷ -2 × 0.6 6. 2.1 × -1.2 + (-44 ÷ 22) − 3.1

8. (- 7 4 ÷ - 3 2 ) + - 5 6 + 53 10. (- 4 3 + -22) ÷ - 8 5 ÷ 10 3 12. -3 1 4 + ( 5 6 × 3 10 ) − (- 7 9 ) + -33

14. -1.5 + ( 4 5 ÷ -22) + 3.6 16. 22 ÷ - 1 2 + 32 − (0.75 − -0.2)

A submarine tracks its descents and ascents.

First, it dives down 45.5 meters. Then, it ascends another 30.5 meters. Finally, it descends another 50.6 meters.

What is the average change in depth?

Hint: To find the average, add up all the distances and divide by the number of distances you added.

A student starts a test with a perfect score of 100 points. She gets 5 questions wrong. Each wrong answer subtracts 2.5 points. However, she gets a bonus question right, which adds 10 points.

What is her final score?

A truck has 15.5 gallons of fuel in its tank.

The truck drives for 4 hours, burning 2.5 gallons of fuel per hour.

The driver then stops at a gas station and adds 8.5 gallons to the tank.

How many gallons of fuel are in the tank now?

One side of a square garden is 4 meters long. Jane uses 6 square meters for flowers and divides the rest of the space into 5 parts for different types of vegetables. How many square meters does she have for each vegetable?

Convert to same form:

1 2 , -0.5, - 1 8 → 0.5, -0.5, -0.125

Compare values:

-0.5 < -0.125 < 0.5

Order from least to greatest. 1. 0.05, 0.55, 1 2 , 0.25 2.1 5 , -0.3, 0.02, 1 8 3.8 9 , -1 1 5 , -1.44, -0.8

Arrange in order:

-0.5, - 1 8 , 0.5

Add or subtract to solve.

Same sign add:3 5 + - 1 5 =4 5

Different sign subtract: 6 7 + - 5 7 = 1 7

Convert subtraction to addition using keep, add, change:1 42 4 =1 4 + - 2 4 =3 4

0.4, - 1 6 , 3 4 ,3 8

0.25, 1 10 , 0.205, 1 9

1 5 + 0.44 =

Multiply or divide to solve.

Same sign → positive

-0.5 × -1.2 = 0.6

Different sign → negative

-0.5 × 1.2 = -0.6

Convert division to multiplication using keep, change, flip: 1 2 ÷ - 2 5 → 1 2 × - 5 2 = -1 1 4

=

A car uses 4 15 a tank of gas for a 30 2 3 mile road trip. What fraction of the tank is used per mile?

Rose started a game with a score of -1 3 4 points. She lost another 2.05 points in the next round. What was her total score?

A person hikes down a mountain at a speed of 2.4 kilometers per hour. How far is he from where he started after 3 5 of an hour?

A submarine is located -3.8 miles below sea level. It rises 5 8 miles. What is the new elevation of the submarine?

Chapter 3

In Chapter 3, we will work with

Algebraic Expressions

Algebraic expressions help us model real-world situations so we can use mathematics to solve problems.

• We will translate words into algebraic expressions.

• We will evaluate expressions.

• We will simplify expressions.

• We will use the distributive property.

• We will factor expressions.

Lesson instructions 1

Write an expression given a verbal statement.

The sum of fifty and a number, divided by nine.

1. Determine what each operation word means.

2. The sum of fifty and a number divided by nine.

3. Assign a variable and write the expression. 50 + n 9 + ÷

Identify the underlined parts of each expression.

1. 5x + 9 × 3y

A. constant

B. variable

C. coefficient

D. term

A. constant

B. variable

C. coefficient

D. term

Write an expression for each statement.

5. Triple n minus -4.2

7. Fourteen less than the quotient of d and 3

9. The product of s and twelve divided by u

11. One-fourth x plus 18 minus 2

A. constant

B. variable

C. coefficient

D. term

A. constant B. variable

C. coefficient

D. term

6. Two increased by g plus 11

8. Three-fifths y subtracted from -6

10. Eleven divided by t minus three

12. The quotient of 20 and z decreased by -10

Write an expression that models each statement.

13. He has five more than 9 times as much as Brendan.

14. The 24 students in the class are divided into some groups.

15. She had twice as many beads as Lisa but lost 18.

Molly is making bracelets to sell. She charges a flat rate of $5 for the materials and $0.25 per minute that she works on assembling the bracelet. Write an expression to find out how much a bracelet will cost after m minutes.

The toy store has a sale going on this week. Each board game costs 8 dollars, and each card game costs 4 dollars. If Darius goes to the store and purchases v board games and c card games, write an expression to determine how much he’d spend in all.

Byron is 4 years older than half his uncle’s age. If his uncle is y years old, write an expression to represent Byron’s age.

An auditorium has two types of seats: general admission and VIP. The number of general admission tickets sold is represented by g, and the number of VIP tickets sold is represented by v. The total number of seats available in the auditorium is 500. Write an expression to represent the number of unsold seats if g and v tickets are sold.

Lesson instructions 2

Evaluate an expression when given values for the variables.

Evaluate -4b – 6c when b = -9 and c = 2.5

1. Substitute the values into the expression. -4(-9) – 6(2.5)

2. Follow the order of operations 36 – 15

3. Simplify. 21

Match each expression with its corresponding value if x = -3, y = 1.8, and z = 5 6 .

1. -8y + x

2. (-15) + xz

3. 9x – 21

4. 6z – 3x

5. 11y -x

6. z(4x2)

Evaluate each expression given the values.

7. x + 3y when x = -2 and y = -10.

8. 4n – m when n = -3.02 and m = 0.9.

9. -a + b when a = - 3 4 and b = 3 2 5 .

Evaluate each expression if a = -2.3, b = 2 5 , and c = 10.

10. -2bc 13. c 2 + 2a

+ a

A. 30

B. -48

C. -17 1 2

D. 6.6

E. -17.4 F. 14

Mary is running a lemonade stand. She charges $1.50 for each cup of regular lemonade and $2.00 for each cup of strawberry lemonade.

A. Write an expression to model how much money Mary can make if she sells r cups of regular lemonade and s cups of strawberry lemonade.

Joe is designing a poster for a school event. He uses x large sheets of paper and y small sheets of paper. Each large sheet covers 5 square feet and each small sheet covers 2 square feet.

A. Write an expression to model how much area the sheets of paper cover.

B. If she sells 12 cups of regular lemonade and 8 cups of strawberry lemonade, how much money did she make?

B. How much area do the sheets cover if Joe uses 4 large sheets and 6 small sheets.

A bakery bakes b batches of cookies. Each batch yields 24 cookies. The bakers then pack the cookies into boxes. Each box can hold c cookies.

A. Write an expression to model how many boxes the bakery needs.

A farmer is building two square pens. The first pen has a side length of x meters, and the second pen has a side length of y meters.

A. Write an expression to model the total area of the two pens.

B. If the bakery bakes 6 batches of cookies and each box holds 12 cookies, how many boxes do they need?

B. If the first pen has a side length of 5 meters, and the second pen has a side length of 8 meters, what is the total area of the two pens?

Lesson instructions 3

Simplify each expression by identifying and combining the like terms.

Simplify: 8x – 19y – 11x + 5 – 13

1. Identify the like terms. 8x – 19y – 11x + 5 – 13

2. Combine the like terms. -3x – 19y – 8

Sort each term into groups of like terms.

Terms

Simplify each expression by combining like terms.

Matt bought 4 green notebooks that each cost x dollars and 10 yellow notebooks that each cost x dollars. He also spent $8 on snacks and $16 on clothes.

Write and simplify an expression for the total amount of money Matt spent at the store.

Amy is y years old. Maddie is 4 times as old as Amy. Bella is 8 years younger than Maddie.

Write an expression to represent the sum of their ages. Simplify the expression by combining like terms.

Barbara and Bessie are crocheting blankets. Barbara has 10.5 inches of her blanket already completed and can crochet at a rate of 5 inches per hour. Bessie has 7 inches of her blanket already completed and can crochet at a rate of 6 inches per hour.

Write and simplify an expression for the total number of inches Barbara and Bessie will have crocheted after h hours.

Manny owes his brother $45. Manny has $18 saved, and his grandpa gave him $10 for his birthday. He can also earn $6 for each lawn that he mows.

Write and simplify an expression for the total amount of money Manny will have after mowing x lawns.

Lesson instructions 4 Use the distributive property to simplify each expression.

-9(-12x + 7)

1. Multiply the outside term by each inside term. (-9)(-12x) + (-9)(7)

2. Simplify the expression. 108x – 63

Simplify each expression using the distributive property.

1. -5(2x + 7) 3. -5(6y – 9)

5.7(-2a + 3.4)

2 5 (-25r + 55)

6(13 – 7t)

1 2 (-4m – 10)

-2.3(4h − 1.5)

7(21 – 17t)

9. Ronald simplified the expression below using the distributive property. Do you agree with his answer? Why or why not?

-7(-5t + 3)

-35t – 21t

Match each expression with its corresponding simplified expression.

10. 4(2x – 3)

11. -4(2x – 3)

12. -4(2x + 3)

13. 2(3x – 4)

14. 3(2x – 4)

15. -2(-2x - 3)

16. -3(4 + 3x)

A. -8x – 12

B. -8x + 12

C. 6x – 12

D. 8x – 12

E. 4x + 6

F. 6x – 8

G. -12 – 9x

A group of friends order dinner. Each pizza costs $12 plus t dollars for extra toppings.

Write and simplify an expression to represent the total cost if they buy 4 pizzas.

The student council is organizing a fundraiser by selling gift bags. Each bag contains x keychains and 5 bookmarks. They plan to prepare 6 gift bags.

Write and simplify an expression for the total number of keychains and bookmarks in all the bags.

A baker is selling boxes of cupcakes. Each box contains 4 chocolate cupcakes plus c vanilla cupcakes.

Write and simplify an expression for the total number of cupcakes if a customer buys 8 boxes.

Lily buys 5 sets of clay that each cost c dollars and a paint set that costs $10. To complete her project, Lily returns to the shop and buys the same things two more times.

Write and simplify an expression to represent the total cost of all the supplies Lily buys.

Lesson instructions 5

Simplify each expression using the distributive property and combining like terms.

Simplify each expression.

19b – 7(12b + 6)

1. Use the distributive property to multiply. 19b – 7(12b) + (-7)(6) 19b – 84b – 42

2. Combine like terms. -65b – 42

1.5(2x + 4.2) – 0.7x – 3.4

3. -4 – 2(5y + 3) + 7y

-0.8(5y – 3.6) + 2.4y – 1.2

5. 5(3c + 1) – 2(4c – 3) + 8

Add each expression to the one next to it and simplify. Write the simplified expression in the rectangle on top of both expressions.

A shipping company is preparing packages. Each package contains b small boxes and 3 large boxes. The company is shipping 7 packages to City A and 5 packages to City B.

Write and simplify an expression to represent the total number of small and large boxes shipped.

A grocery store stocks 5 bottles of juice and c cans of soda on each shelf in Aisle 1 but only 2 bottles of juice and c cans of soda on each shelf in Aisle 2. There are 12 shelves in Aisle 1 and 9 shelves in Aisle 2.

Write and simplify an expression to represent the total items stocked.

A charity organization is preparing gift baskets for a fundraiser. Each basket contains g large items and 3 small items. They make 8 identical baskets for donors and are left with 2 extra small items.

Write and simplify an expression for the total number of items the organization has.

Each of the 10 children at a daycare eats s snacks and drinks 2 bottles of water each morning. In the afternoon, each child has 2 times the amount of snacks they had in the morning and another bottle of water.

Write and simplify an expression for the total number of snacks and water consumed at the daycare each day.

Lesson instructions 6 Factor each expression by finding the greatest common factor (GCF).

33p + 55

1. Determine the GCF of all terms. GCF = 11

2. Use the area model to divide.

3. Write the factored expression. 11(3p + 5) 3p 33p 55 11 55

Determine if each statement is true or false. Circle the correct answer.

10 is a factor of 30x + 50 T or F

3. 2 is a factor of 5x + 10 T or F

-12 is a factor of 60h – 36 T or F

Factor each expression.

4. 6y is a factor of 15y + 6x + 12 T or F

6. -3 is a factor of -9x + 6y − 12 T or F

18.

+ 210p - 140 2. 8t is a factor of -40t + 16 T or F

The entrance fee at a museum for one adult ticket is $12, and the price for one child’s ticket is $8. Write an expression to model how much money the museum makes when they sell x adult tickets and y child tickets. Then, factor the expression.

A farmer is selling fruit at a market. He has x boxes of apples, and each box contains 24 apples. He has y boxes of oranges, and each box contains 36 oranges. Write and factor an expression to model the total number of pieces of fruit the farmer has.

A shipping company is organizing packages for two different routes. Route 1 has x trucks, each carrying 50 packages. Route 2 has y trucks, each carrying 35 packages.

Write and factor an expression to model the total number of packages the company is shipping.

A school is organizing two different fundraising events. Event 1 has x tables, with each table selling 40 tickets. Event 2 has y tables, with each table selling 60 tickets.

Write and factor an expression to model the total number of tickets sold across both events.

Match each statement with its corresponding expression.

The product of a number and 7, decreased by 5

multiply x subtract

1. Seven more than the sum of a number and 5

2. Five times the difference of a number and 7

3. The quotient of a number and 5, plus 7

4. Seven times a number subtracted by five times a number

5. Five divided by a number minus 7

Evaluate each expression if p = -5, q = 3 5 , and r = -0.4.

7p + 2r

1. Substitute the values into the expression. 7(-5) + 2(-0.4)

2. Use order of operations. -35 – 0.8

3. Simplify. -35.8

Simplify each expression.

19b – 7(12b + 6)

1. Use the distributive property to multiply. 19b – 7(12b) + (-7)(6) 19b – 84b – 42

2. Combine like terms. -65b – 42

Factor each expression.

12x + 24

1. Find the GCF (greatest common factor) 12

2. Divide both terms by the GCF. 12(x + 2)

+ 27

+ 44

– 70

Use the problem to answer questions 1-4.

Sarah is planning a party. She wants to buy party hats, balloons, and a cake. The cost of the party hats is $2 each, the balloons cost $1 each, and the cake costs $15. Sarah plans to buy x party hats and y balloons and one cake. Additionally, she needs to pay a delivery fee of $5 for the entire order.

Write an expression to show the total cost of the party supplies.

Combine like terms to simplify the expression.

If Sarah buys 9 party hats and 4 balloons, how much will it cost her?

If Sarah buys 20 party hats and 6 balloons, how much will it cost her?

Chapter 4

In Chapter 4, we will learn about

Equations and Inequalities

Now we can apply what we have learned about expressions to help us solve equations and inequalities.

• We will solve one-step and two-step equations and inequalities using the four basic operations.

• We will write and solve equations and inequalities for real-world situations.

the

Solve each equation using inverse operations. 9x = 36

the

Samantha has m marbles. She buys 53 more marbles, bringing her total to 96. Write and solve an equation to find out how many marbles Samantha started with.

A warehouse had x items in stock. After shipping out 3,250 items, 1,750 items remain. Write and solve an equation to find how many items were originally in stock.

A farmer grows 200 apple trees on each of his f farms. If the total number of apple trees across all farms is 6,000, write and solve an equation to find how many farms there are.

A printing company has p pages to print. If each printer prints 24 pages per hour and the printers work 500 hours in total, write and solve an equation to find how many pages the company has to print in all.

Lesson instructions 2

Solve each two-step equation. 2x + 8 = 30 1. Undo the addition/subtraction. 2. Undo the multiplication/division.

Solve each two-step equation. Check your solution.

Kevin is buying s shirts. Each shirt costs $12. He also buys a hat for $5. If he spends a total of $41, how many shirts did he buy?

Daniel needs to buy some markers. He has $30, and each marker costs $4. After buying some markers, m, he has $6 left. How many markers did he buy?

Tori spends 1 2 of her paycheck, p, on new clothes and $12 on food. If Tori has $546 left after her spending, how much did she earn from her paycheck?

A group of 6 friends is sharing the cost, c, of a road trip. Each friend has to pay an additional $15 for gas. If each friend ends up paying $40 altogether, what is the total cost of the road trip?

Write and solve an equation to represent the real-world scenario.

Carlos went bowling. He paid a $5 entry fee and $3 per game he played. If he spent a total of $26, how many games did he play?

1) Write the equation. 5 + 3x = 26

2) Undo the addition/subtraction. 3x = 21

3) Undo the multiplication/division. x = 7

4) Interpret the answer. 7 games

Solve each two-step equation. Check your solution.

1. A delivery service charges a base fee of $50 for a delivery, plus $0.75 per item delivered. The total cost for a delivery was $350. How many items did the customer have delivered?

2. Mr. Johnson bought a set of paintbrushes and divided them evenly among his 5 art students. He also gave each student 3 customized paint brushes with their names on them. If each student ended up with 22 paintbrushes, how many brushes were in the set?

3. A group of 4 friends shared a bag of candies evenly. Each friend also ate 4 candies from their own stash. If each friend ended up eating 12 candies total, how many candies were in the bag?

4. Jack is renovating his house. He spent $34 per hour on labor and $24 on initial supplies. If the total cost of the renovation was $228, how many hours of labor did he pay for?

A printing business charges a flat setup fee of $100 for any order. In addition, they charge $0.25 per page for printing. A customer orders pages, and the total cost is $225. Write an equation to represent the total cost of the printing order, and solve to figure out the number of pages printed.

An employee works at a company where they earn a salary of $500 per week, plus $20 for every hour of overtime worked. If the employee worked overtime hours and earned a total of $700, write an equation to represent the total salary. Solve for the number of overtime hours worked.

A group of 6 friends split the cost of a party. Each friend also paid $30 towards a gift. If each friend paid $360, how much did the party cost? Write and solve an equation.

Sally, Molly, and Briana decided to buy and share a pack of erasers. Each girl ended up giving 2 erasers away and were left with 16. Write and solve an equation to determine how many erasers were in the pack.

Lesson instructions 4

Solve and graph the inequality.

Check your solution. 1. Use inverse operations.

Graph each inequality.

Solve and graph each inequality. Check your solution.

2. Graph on a number line.

A water jug can hold at most 64 ounces of water. If it already contains 48 ounces, how much more water can be added to the jug? Write, solve, and graph an inequality to represent this situation.

Laura is hosting an event. She has a maximum of 120 seats. If she has already invited 56 people, how many more people can she invite? Write, solve, and graph an inequality to represent this situation.

Carlos is tracking his steps and wants to walk at least 10,000 steps today. If he has already walked 7,200 steps, how many more steps does he need to meet his goal? Write, solve, and graph an inequality to represent this situation.

Mrs. Harris is sharpening pencils for her classes. She needs to sharpen a minimum of 120 pencils to have enough for all her students. If she has already sharpened 85 pencils, how many more does she need to sharpen? Write, solve, and graph an inequality to represent this situation.

Lesson instructions 5

Solve and graph the inequality. Check your solution.

Multiply or divide both sides to solve. Flip the inequality symbol when multiplying/dividing by a negative number on both sides.

Solve each inequality. List 3 possible solutions. Then, choose one solution for each problem to check your work.

Possible solutions: Possible solutions: Possible solutions:

Solve and graph each inequality. Check your solution.

10. Remi solved the following inequality. Do you agree with her solution? Why or why not.

Kayla wants to ensure that she spends no more than $360 on groceries in 8 weeks. Write, solve, and graph an inequality to determine the maximum amount, m, she can spend per week.

A school performance charges $75 per ticket. They need to sell at least $6,000 worth of tickets to make money on the show. Write and solve an inequality to find the minimum number of t tickets they need to sell.

A shipping company is dividing p pounds of cargo evenly among 12 boxes. Each box can hold no more than 50 pounds. Write and solve an inequality to determine the maximum number of pounds of cargo.

A group raised d dollars and plans to divide it evenly among 20 participants. If each participant should receive at least $25, how much money must the group raise?

Lesson instructions 6

Solve and graph each inequality. Check your solution.

1. Apply inverse operations to addition/subtraction.

2. Apply inverse operations to multiplication/division. Don’t forget to flip the inequality symbol if multiplying or dividing by a negative number.

3. Graph.

Solve and graph each inequality. Check your solution.

7. Brady solved and graphed the following inequality. Do you agree with his solution? Why or why not.

8. Cora solved and graphed the following inequality. Do you agree with her solution? Why or why not.

Sarah is saving money to buy a new desk. She already has $150 saved, and the desk she wants costs at least $400. Sarah plans to save $50 each week. Write, solve, and graph an inequality to represent how many weeks, w, it will take her to save enough money to buy the desk.

Martha is planning an event and has a budget of $100. The cost of renting the hall is $60, and each guest costs $5 for food. Write, solve, and graph an inequality to determine the maximum number of guests Martha can invite while staying within the budget.

Alex has a collection of b books. He evenly divides the books into 5 shelves for his reading nook. He lets his brother borrow 3 books from each shelf. If Alex wants at least 12 books on each shelf after his brother borrows the books, what could the total number of books in Alex's collection be?

Nine friends evenly split the cost, c, of art supplies. Each friend also paid $6 for a personalized case. If each friend wants to spend no more than $35, how much could the total cost of art supplies be?

Write and solve an inequality for the word problem.

Max went ice skating. He paid a $6 entry fee and $2 per hour he skated. If he wanted to spend less than $20, how many hours could he skate? Could he skate for 5 hours? Explain.

1. Write the inequality.

6 + 2h < 20

2. Undo the addition/subtraction. 2h < 14

3. Undo the multiplication/division. h < 7

4. Use your solution to answer the question. Yes. 5 < 7, so 5 hours works.

Write and solve an inequality for each word problem.

1. Maria is buying landscaping supplies. A bag of soil costs $6, and each plant costs $12. If she has at most $150 to spend, write an inequality to show how many plants Maria can buy. Can Maria buy 11 plants? Explain.

2. Sara plants trees evenly across 5 plots. After planting, she adds 3 more trees to each plot. If each plot ends up with more than 20 trees, write an inequality to show how many trees she could have planted at first. Could she have planted 80 trees? Explain.

3. A group of friends is taking a road trip. They have already spent $200 on accommodations, and they estimate gas will cost $25 per hour of driving. If their budget is no more than $500, write an inequality to show how many hours they can drive. Can they drive for 12 hours? Explain.

4. A carpenter divides wooden planks equally among 8 birdhouses. Later, she takes away 3 planks from each birdhouse. If each birdhouse has fewer than 10 planks, write an inequality to show how many planks she could have started with. Could she have started with 100 planks? Explain.

A warehouse receives a shipment of boxes, which are evenly stacked on 6 shelves. Later, 4 more boxes are added to each shelf. If each shelf has at least 10 boxes, how many boxes were in the shipment? Write and solve an inequality to represent this situation.

Could there be 36 boxes in the shipment? Explain.

A moving company charges $30 per item and a flat $60 transportation fee. If the total cost must be no more than $240, how many items can a customer ship? Write and solve an inequality to represent this situation.

Could the customer ship 7 items? Explain.

A local club earns $250 from donations. They also sell t-shirts for $10 each. If the club needs to raise more than $700, how many t-shirts must they sell? Write and solve an inequality to represent this situation.

Could they sell 45 t-shirts? Explain.

A group of friends divides cards evenly among 4 people. Each person also gives 3 cards to their younger sibling. If each person ends up with a minimum of 9 cards, how many cards were divided to start? Write and solve an inequality to represent this situation.

Could they have started with 48 cards? Explain.

Solve each one-step equation. Check your solution.

8x = 16

1. Use inverse operations. 8x = 16 ÷ 8 ÷ 8

2. Write the solution. x = 2

Solve each two-step equation. Check your solution.

2x – 4 = -6

1. Undo addition/subtraction. 2x – 4 = -6 + 4 + 4

2. Undo multiplication/division. 2x = -2 ÷ 2 ÷ 2

3. Write the solution. x = -1

Solve each one-step inequality. Graph your solution.

-3x = -18

1. Use inverse operations. Flip the sign if you multiply or divide by a negative number.

-3x > -18 ÷ -3 ÷ -3

2. Write and graph the solution. x < 6

Solve each two-step inequality. Graph your solution.

-8x + 4 ≥ 20

1. Undo addition/subtraction. -8x + 4 ≥ 20 - 4 - 4

2. Undo multiplication/division. -8x ≥ 16 ÷ -8 ÷ -8

3. Write and graph the solution. x ≤ -2

Emma earns $12 per hour babysitting. She also earned a $20 tip from one of her clients. If she made $92 total, how many hours did she work?

A group of 6 friends started with a box of candy that they split evenly. Afterwards, they each gave away 2 pieces of candy to a sibling. If each friend ends up with 7 pieces of candy, how many pieces of candy did the box start with?

Carlos wants to save at least $245 for a new bike. He already has $80 saved and earns $15 per hour at his part-time job. Write and solve an inequality to determine how many hours he needs to work.

A suitcase can hold a maximum of 50 pounds. Jenny’s suitcase already weighs 18 pounds, and she wants to pack some pairs of shoes that each weigh 4 pounds. Write and solve an inequality to find how many pairs of shoes she can bring.

Chapter 5

In Chapter 5, we will expand on

Ratios, Rates, and Proportions

Proportional relationships are found in real-world situations such as baking, driving, and economics.

• We will find unit rates and use them to find equivalent ratios.

• We will solve proportions to find equivalent ratios.

• We will set up and solve proportions to model realworld situations.

• We will model proportional relationships using tables, graphs, and equations and identify their key features.

Match each statement to its unit rate.

826.2 miles in 45 hours

Find the unit rate. Write the answer in words.

6. 52 miles on 1.3 gallons 7. 136 words in 10 minutes

8. 98 beats in 1 2 5 minutes

$493.50 per 10.5 months

Find the unit rate. Write the answer as a fraction. 1. 46.75 miles in 5.5 hours 2. 65 1 2 miles in 3 hours

10. 28.75 gallons in 6.25 minutes

11.

for 3 pounds of apples

A team builds 262.5 feet of fence in 17.5 hours. What is the speed at which they build?

A car travels 487.2 miles using 16.8 gallons of gas. How many miles per gallon does the car get?

A cake recipe requires 4 1 2 cups of flour for 3 3 4 dozen cupcakes. How many cups of flour per dozen cupcakes is required?

A painter can paint 15 3 10 square feet in 2 1 4 hours. How many square feet per hour can the painter paint?

Lesson instructions 2

Compare ratios using unit rates.

Circle all equivalent ratios.

Which is the better buy? $5 for 2 cups OR $6 for 3 cups

5. Rice

A. 5 pounds for $7.50

B. 10 pounds for $13.80

C. 20 pounds for $29.00

7. Soap

A. 32 ounces for $3.84

B. 64 ounces for $8.96

C. 96 ounces for $12.48

9. 90 gallons in 30 minutes

The second option is the better buy because each cup costs less.

6. Snack Packs

A. 8 pack for $6.40

B. 12 pack for $8.88

C. 20 pack for $13.80

8. Gasoline

A. 5 gallons for $21.75

B. 10 gallons for $41.50

C. 15 gallons for $59.10

gallons in 15 minutes

10. 400 bricks in 5 hours 300 bricks in 3 hours

11. $18 for 6 items $27 for 9 items

12. 25 miles in 10 minutes

13. 15 liters in 3 hours

14. $350 for 14 hours

miles in 6 minutes

liters in 5 hours

Justin pays $21 for 3 months of a magazine subscription. Henry pays $40 for 5 months of a magazine subscription. Who pays more per month? How much more?

Callie’s recipe calls for 6 tablespoons of butter for 1.5 cups of flour. Tina’s recipe calls for 8 tablespoons of butter for 3 cups of flour. Whose recipe uses more tablespoons of butter per cup of flour?

Rose waters two garden plots in her backyard. The first plot has 9 plants and requires 18 liters of water. The second plot has 12 plants and requires 36 liters of water. Which plot requires more water per plant?

The A Train traveled 120 miles in 4 hours. The B Train traveled 150 miles in 6 hours. Which train went faster?

Solve the proportion with cross multiplication. Multiply. Divide.

A hiker walks 6 miles in 2 hours. How far will the hiker walk in 5 hours at the same pace?

A hose fills 48 gallons of water in 8 minutes. How many gallons will it fill in 20 minutes at the same rate?

A chef can wash 15 dishes in 10 minutes. How many dishes can the chef wash in 30 minutes at the same rate?

A factory produces 240 toys in 6 hours. How many toys will it produce in 15 hours at the same rate?

Match each scenario to its proportion.

1. Donna bakes 8 cookies in 12 minutes. How many minutes will it take her to bake 20 cookies?

2. Victor completes 6 math problems in 5 minutes. How many math problems can he complete in 15 minutes?

3. Mannie can paint 8 walls in 12 minutes. How many walls can he paint in 20 minutes?

4. A baker makes 15 cupcakes in 5 minutes. How long does it take for her to bake 6 cupcakes?

5. A runner covers 12 miles in 20 minutes. How many miles can he cover in 8 minutes?

6. A train travels 15 miles in 6 minutes. How long will it take to travel 5 miles?

Fill in the table.

7. A coffee shop uses 3 cups of milk to make 2 cups of coffee. How many cups of milk are needed to make 10 cups of coffee? cups of milk cups of

8. A runner covers 5 miles in 0.5 hours. How many miles will the runner cover in 2 hours?

9. A painter paints 8 walls in 4 hours. How long will it take him to paint 12 walls?

A water pump fills 300 gallons in 15 minutes. How many gallons will it fill in 40 minutes?

A printer prints 120 pages in 8 minutes. How many pages can it print in 15 minutes?

A teacher grades 24 papers in 30 minutes. How many papers can be graded in 120 minutes?

A machine produces 75 parts in 5 minutes. How many minutes does it take to produce 30 parts?

Determine if relationships are proportional by looking for a consistent unit rate.

The relationship between the number of notebooks and the cost is proportional because the unit rate is always $7 per notebook. Notebooks 1 5 8 10

Calculate the ratios in each table. Then circle if the relationship is proportional or not proportional.

proportional not proportional proportional not proportional proportional not proportional proportional not proportional

Circle if the relationship is proportional or not proportional.

Each bus seats 40 passengers.

Buses

Passengers

A. Fill-in the table.

B. Find the unit rate of each ratio.

C. How many buses will be needed for 680 passengers?

D. Is the relationship proportional?

Each roll has 110 stamps.

Stamps

A. Fill-in the table.

B. Find the unit rate of each ratio.

C. How many rolls would be needed to get 4,510 stamps?

D. Is the relationship between the number of rolls and the number of stamps proportional?

Danny eats 2 cookies every time his mom makes a batch.

A. Fill-in the table.

B. Find the unit rate of each ratio.

C. How many cupcakes are left when Danny’s mom makes 36 cupcakes?

D. Is the relationship proportional? Each shelf holds 30 books.

Shelves 6 15 18

Books

A. Fill-in the table.

B. Find the unit rate of each ratio.

C. How many shelves are needed to hold 810 books?

D. Is the relationship between the number of shelves and the number of books proportional?

Lesson instructions 6 Find the constant of proportionality (k) by dividing y by x. Then, write the equation.

Match each table to an equation.

= 3 Equation: y = 3x

y = 12x

y = 4x

y = 1 5 x

y = -2x

y = 0.7x

y = 19x

Determine the constant of proportionality (k) and write an equation.

A recipe uses 3 cups of sugar to make 48 cupcakes. If you want to keep the ingredients in proportion so that the cupcakes taste the same, write an equation to model how many cupcakes (y) would be made with x cups of sugar.

It cost $22.50 for five tickets to the museum. If the cost of the tickets remains the same no matter how many you buy, write an equation that could be used to find the cost (y) for any number of tickets (x).

Hannah uses 7.5 yards of fabric to make 3 shirts. Write an equation to model the yards of fabric (y) needed for any number of shirts (x).

A painter covers 800 square feet with 5 gallons of paint. Given that he always uses the same number of gallons per square foot when he paints, write an equation that could be used to calculate how many gallons (y) would be used for any number of square feet (x).

What is the meaning of the point (4, 240) on the graph?

What is the meaning of the point (6, 132) on the graph?

What is the meaning of the point (8, 2) on the graph?

What is the meaning of the point (25, 5) on the graph?

Find the constant of proportionality of proportional relationships represented in different ways.

Match each proportional relationship to its constant of proportionality.

Determine if the information represents a proportional relationship.

A car traveled 180 miles using 6 gallons of gas. If the distance traveled is directly proportional to the amount of gas used, what is the constant of proportionality?

A printer produced 1,500 pages in 30 minutes. If the number of pages printed is directly proportional to the time in minutes, what is the constant of proportionality?

A juice factory made 720 bottles of juice from 8 crates of fruit. If the number of bottles is directly proportional to the number of crates, what is the constant of proportionality?

An orchard produced 640 oranges from 20 trees. If the number of oranges is directly proportional to the number of trees, what is the constant of proportionality?

Find the unit rate.

$3 for 15 oranges 3. 400 gallons in 5 days

Determine if the two ratios are equivalent.

576 widgets in 12 hours 5. 120 miles in 2 hours and 360 miles in 6 hours

6. 540 pages in 9 minutes and 3280 pages in 5 minutes 7. 100 liters in 4 hours and 250 liters in 10 hours 8. 30 cupcakes in 6 minutes and 46 cupcakes in 10 minutes

Determine if the relationship is proportional. If so, find the constant of proportionality.

Maria is practicing her typing skills. She tracks the number of words she types per minute and records the data in a table.

Leo is filling a bucket with water at a constant rate. He keeps track of the amount of water added over time.

Assuming the relationship is proportional, write an equation to determine the total number of words typed (y) based on time in minutes (x).

Write an equation to determine the total amount of water in liters (y) based on time in minutes (x).

What is the meaning of the value (4, 3) based on the graph?

A. It takes 3 days to read 4 books.

B. One book takes 4 days to read.

C. It takes 4 days to read 3 books.

What is the meaning of the value (5, 100) based on the graph?

A. It cost $100 for 5 hours of the day.

B. After working 100 hours, $5 is earned.

C. After working 5 hours, $100 is earned.

Chapter 6

In Chapter 6, we will expand on

Percents

Percents show how many parts out of 100 to make it easy to compare things like grades and prices.

• We will convert between percents and decimals.

• We will use proportions and the percent equation to solve real-life problems involving percents.

• We will calculate percent of change.

• We will learn about markup, discount, tax, tip, commission, and simple interest.

Convert each decimal to a percent and each percent to a decimal.

Percents to Decimals Move the decimal two places to the left.

Match each decimal with its equivalent percent.

Decimals to Percents Move the decimal two places to the right.

Convert each decimal to a percent.

Convert each percent to a decimal.

A farmer harvested 70.25% of his apple crop this season. Express that percentage as a decimal.

Judy completed 90.3% of her math homework. Express this percentage as a decimal.

At a performance, 0.92 of the seats were filled. What percent of the seats were filled?

In a garden, 0.408 of the plants were roses. What percent were roses?

Find the missing part, whole, or percent with a proportion.

Solve for the missing part.

What is 25% of 80?

What number is 25% of 44? % 100 = part whole 25 100 = x 44

100x = 25(44) 100x = 1100 x = 11

What is 28% of 25?

What is 12% of 50?

What is 40% of 80?

Solve for the missing whole.

10. 14 is 35% of what number? 11. 17 is 34% of what number? 12. 16 is 40% of what number?

Solve for the missing percent. 16. 45 is what percent of 75? 19. 27 is what percent of 90?

9 is what percent of 36?

16 is what percent of 50?

21 is what percent of 70?

52 is what percent of 80?

Use a proportion to solve.

22. What is 55% of 120? 23. 12 is 80% of what number?

27 is what percent of 60?

In a bakery, there are 18 chocolate cupcakes. These 18 cupcakes make up 20% of all the cupcakes baked that day. How many cupcakes were baked in total?

At a school performance 40% of the 200 tickets sold were for students of that school. How many tickets were sold to students of the school?

At a pet store, 14 bunnies are available for sale, and these bunnies make up 35% of all the animals in the store. How many animals are available for sale?

A grocery store has 250 items on sale, and 10% of them are organic. How many organic items are on sale?

Lesson instructions 3

Find the missing part, whole, or percent with the percent equation.

Solve for the missing part.

1. What is 25% of 80?

2. 25 is 80% of what number?

3. 25 is what percent of 80?

4. What is 40% of 90?

5. 40 is what percent of 90?

6. 40 is 90% of what number?

Solve for the missing part.

7. What is 20% of 150?

9. 30% of what number is 60?

11. 32 is what percent of 128?

13. 38 is 40% of what number?

15. 4.5 is what percent of 36?

17. 45 is 60% of what number?

19. 14 is 35% of what number?

part = percent • whole

What number is 25% of 44?

part = 0.25 • 44 part = 11

A. 40 = p • 90

B. 40 = 0.90 • b

C. 25 = p • 80

D. a = 0.25 • 80

E. a = 0.40 • 90

F. 25 = 0.80 • b

8. 21 is 30% of what number?

10. What is 22.5% of 64?

12. What is 70% of 26?

14. 51 is what percent of 85?

16. What is 16% of 175?

18. 42 is 14% of what number?

20. 15.4 is what percent of 28?

A bag contained 120 marbles, and 90 of them were red. What percent of the marbles were red?

At a performance, 72 seats were occupied, and this represents 80% of the total number of seats. How many seats does the auditorium have?

In a company, 30% of the 200 employees are part of the design team. How many employees are in the design team?

James earns $3,000 per month. He spends $900 of that specifically on rent. What percent of his monthly income goes toward rent?

Lesson instructions 4

Solve the realworld percent problems by using the appropriate equation.

Price Markup: Original Price + (Original Price × Percent)

Discount: Original Price - (Original Price × Percent)

Taxes: Original Cost + (Original Cost × Percent)

Tips: Original Bill + (Original Bill × Percent)

Choose the correct equation that matches the total.

1. 5% tax on $45

A. 45 + (45 × 0.50)

B. 45 − (45 × 0.05)

C. 45 + (45 × 0.05)

4. 16% off of $40

A. 40 − (40 × 0.16)

B. 16 − (40 × 0.16)

C. 40 + (16 × 0.40)

8% tax on $525

A. 525 + (0.08 x 525)

B. 525 × 0.08

C. 525 ÷ 0.08 5. 50% markup on $90

A. 90 + (90 × 1.50)

B. 90 − (90 × 0.15)

C. 90 + (90 × 0.5) 3. 12% tip on $89 bill

A. 89 − (89 × 0.12)

B. 89 + (89 × 1.2)

C. 89 + (89 × 0.12)

6. 11% tax on $450

A. 450 − (450 × 0.11)

B. 450 × 1.1

C. 450 + (450 × 0.11)

Find the price after the tax or tip.

7. 18% tip on $56 bill 9. 6% tax on $200 bill

tip on $105 bill

Find the price after the discount is applied.

25% off of $180

of $72

off of $52

A car dealership purchases a used car for $18,000 and marks it up by 15% before selling it. What is the final sale price?

A keyboard usually costs $200.00 and is offered at a 52% discount. What is its final price after the discount?

A mattress is priced at $350.00, and a sales tax of 8% is applied. What is the total cost of the mattress?

Mike’s dinner bill was $80.00 before the tip. He decided to give a 15% tip. What is the total amount paid?

Lesson instructions 5

Solve for percent of change or percent of error.

Percent of Change = |New Value - Original Value| Original Value × 100

Percent of Error = |Estimated Value - Actual Value| Actual Value × 100

Determine if each percent change is an increase or decrease.

1. 45 minutes to 60 minutes

3. 50 inches to 48 inches

5. 20 gallons to 18 gallons 2. 1,500 trees to 1,200 trees 4. $9.00 to $11.25 6. 75 chairs to 82 chairs

Match the values to their percent of change.

7. Original Value: 80 New Value: 92

8. Original Value: 50 New Value: 38

9. Original Value: 45 New Value: 54

10. Original Value: 120 New Value: 108

A. 24% decrease

B. 20% increase

C. 15% increase

D. 10% decrease

Find the percent change. Say if it is a percent increase or decrease.

11. The length of a string was originally 80 cm but was cut to 72 cm long.

12. The temperature recorded in the morning was 48OF. In the afternoon the temperature recorded was 60OF.

13. A student’s score on an exam was 66 the first time she took it. The second time she scored a 99.

14. The price of a toaster oven was originally $160 but went on sale for $120.

A factory produces 1,000 cars in January. In February, the factory produces 800 cars. What is the percent change in production from January to February?

A student predicts that he will finish his exam in 75 minutes, but it ends up taking him 100 minutes. Calculate the percent error in his time estimate.

A notebook originally was priced at $3.00. Due to rising production costs, the price increases to $4.20. What is the percent change in the price of the notebook?

A scientist predicts that a chemical reaction will complete in 12 minutes. However, during the experiment, the reaction actually takes 15 minutes. What is the percent error in the scientist’s estimate?

Principal: $280 Interest Rate: 8% Time: 9 months

Principal: $90 Interest Rate: 20% Time: 3 months

A loan of $750 is taken out with simple interest at a rate of 3% per year. If the loan is repaid after 3 years, how much interest will be due in total?

Jack deposits money into a savings account that earns simple interest at a rate of 5% per year. If he leaves the money in the account for 4 years and earns $160, how much was his initial deposit?

David places $900 in a savings account with a simple interest rate. If he leaves his money in the account for 4 years and earns $144, how much is the interest rate?

Rachel invests $3,500 at a simple interest rate of 5% per year. How long will it take for her to earn $350, on her investment?

Use a proportion to find the percent.

1. What is 15% of 60?

What is 25% of 40?

25 100 = x 40 x = 10

10 is 25% of 40

2. 12 is what percent of 125?

3. 18 is 60% of what number?

4. What is 45% of 90?

5. 8 is what percent of 20?

Use the percent equation to solve.

6. 45 is what percent of 120?

part = percent • whole a = p • b

18 is what percent of 90?

18 = p • 90 p = 0.2 = 20%

7. What is 18% of 50?

8. 60 is 75% of what number?

9. 90 is what percent of 150?

10. What is 5% of 80?

Calculate the percent of change. New Value - Original Value Original Value × 100

|3.50 - 5.00| 5.00 × 100 30% decrease

Solve for the simple interest. I = P •

t I = $450 • 0.03 • 5 I = $67.50

11. Original Value: 25 New Value: 45

12. Original Value: 120 New Value: 84

13. Original Value: 48 New Value: 27

14. Original Value: 95 New Value: 38

15. Original Value: 80 New Value: 16

16. Principal: $50 Rate: 5% Time: 7 years 17. Principal: $320 Rate: 7% Time: 6 years

18. Principal: $1,600 Rate: 1.2% Time: 10 years

19. Principal: $73 Rate: 8% Time: 18 years

20. Principal: $1,890 Rate: 12% Time: 15 years

A store buys a watch for $230 and marks up the price by 25% before selling it. What is the price of the watch after markup?

Tom buys a pair of shoes for $90 before tax. The sales tax rate is 6%. What is the total price of the shoes with tax?

A bicycle originally costs $300, but it is on sale for 15% off. What is the sale price of the bicycle after the discount?

John’s dinner bill comes to $48, and he wants to leave an 18% tip for the waiter. What is the total cost of the bill with tip?

Chapter 7

In Chapter 7, we will investigate concepts in

Geometry

The study of shapes includes how to draw them, change them, and compare them, as well as how to calculate their angles, areas, and perimeters.

• We will scale images and redraw them using a scale factor.

• We will identify complementary, supplementary, vertical, and adjacent angles and use them to write equations.

• We will construct triangles.

• We will identify cross sections of 3D shapes.

• We will calculate area and circumference of circles.

Lesson instructions 1

Find the scale factor and missing side.

1. Determine the scale ratio and scale factor by looking at the matching sides.

Scale Ratio: 2 : 10 = 1:5

Scale Factor: 10 2 = 5

2. Use a proportion to find the missing side.

Find the scale ratio and the scale factor.

Scale Ratio =

Scale Factor =

Scale Ratio =

Scale Factor =

Find the missing side using the scale ratio or the scale factor.

Scale Ratio =

Scale Factor =

A rectangular playground is 100 meters long and 50 meters wide. A scale model of the playground is being made using a scale factor of 25:1. What are the dimensions of the playground on the model?

A rectangular garden has a length of 16 feet and a width of 12 feet. A drawing of the garden has a length of 4 inches. What is the width of the garden on the blueprint?

A company’s logo is shaped like a pentagon with a side length of 12 cm. They want to enlarge it for a poster by a scale factor of 6. What is the length of the enlarged side?

A triangular trail has a base length of 200 meters and a height of 160 meters. A map of the trail is drawn using a scale factor of 40:1. What are the base and the height of the triangular trail on the map?

Lesson instructions 2

Create a scale drawing given the scale factor. Determine the new area.

Scale Factor = 2

1. Multiply each side by the scale factor. 2 × 2 = 4 4 × 2 = 8 2. Area = base x height. 4 × 8 = 32 units2

Create a scale drawing of each shape given the scale factor.

Find the area of each shape given the dimensions and scale factor. 1.

Create a scale drawing of the shape below given a scale factor of 4. Find the area of each shape.

Create a scale drawing of the shape below given a scale factor of 1 3 . Find the area of each shape.

=

=

Create a scale drawing of the shape below given a scale factor of 2. Find the area of each shape.

Create a scale drawing of the shape below given a scale factor of 1 2 . Find the area of each shape.

=

Lesson instructions 3

Measure and classify the angle. Find the missing angle.

1. Measure using a protractor. 60º

2. Classify the angle. acute

3. Add or subtract to find the missing angle. 60 – 39 = 21

Measure each angle with a protractor, and then classify it as acute, obtuse, right, or straight.

Draw each angle with a protractor.

Find each missing angle.

Katie is looking at a large clock tower. The minute hand is pointing at the 12, and the hour hand is pointing at the 3.

A. Draw the angle formed by the two clock hands.

Jake is riding his bike on a straight path. He turns left at an intersection, making an 80° turn.

A. Draw the angle Jake turned.

B. Classify the angle as acute, right, obtuse, or straight.

B. Classify the angle as acute, right, obtuse, or straight.

Lily is setting up a tent. One of the support poles forms a 50° angle with the ground, and the other support pole forms a 35° angle with the first pole.

A swing set frame forms a 140° angle at the top. One of the side bars makes a 75° angle with the top beam.

What is the total angle formed by the two poles?

What is the missing angle formed by the other side bar?

Lesson instructions 4 Classify each set of angles. Find the missing angle measure.

1. Classify the pair of angles. complementary

2. Subtract to find the missing angle measure.

Determine if each set of angles is complementary or supplementary.

Find each missing angle measure.

Determine if each set of angles is adjacent or vertical.

Find each missing angle measure.

At an intersection, two roads cross each other, forming four angles. One of the angles measures 65°. What is the measure of the angle that is vertical to it? Explain how you found your answer.

Laura is designing a rectangular picture frame. One of the corners is made up of two adjacent angles: one angle is 35°, and the other angle is unknown. If the two angles form a right angle, what is the measure of the missing angle?

Emma opens a door so that it forms a 110° angle with the wall. If the two angles created are supplementary, what is the measure of the other angle?

A clock shows a time where the minute hand and hour hand form a 96° angle. How many more degrees do they need to form a supplementary angle? How do you know?

Lesson instructions 5 Write and solve an equation to find the missing value.

1. Determine the relationship between the angles. Complementary

2. Write and solve the equation.

3. Plug in x to find the missing angle. 3(22) = 66° 24 + 3x = 90 - 24 - 24 3x = 66 ÷ 3 ÷ 3 x = 22

Write and solve an equation to find the missing angle measure.

Cam wrote and solved an equation for the problem below. Do you agree with his work? Why or why not?

Bella wrote and solved an equation for the problem below. Do you agree with her work? Why or why not?

A window frame is divided into four sections by two crossing bars as shown below. One of the angles is 2x°, and the angle across from it is 75º. Write and solve an equation for x.

A book stand holds a book at an angle as shown below. The support forms one angle of x°, and the base forms another angle of 65°. Write and solve an equation to find the angle at which the book is leaning.

Lesson instructions 6

Tell whether the set of side lengths can make a triangle. Justify your answer.

Ex. 9 in, 5 in, 3 in.

1. Add up each pair of sides to see if the sum is larger than the third side.

9 + 5 > 3 9 + 3 > 5 5 + 3 > 9

2. Write and justify the answer.

No, these side lengths cannot make a triangle because 5 + 3 = 8 which is not larger than 9.

Tell whether each set of side lengths can make a triangle. Justify your answer.

1. 19 ft, 27 ft, 33 ft

3. 25 in, 31 in, 4 in

5. 25 ft, 30 ft, 40 ft

22 m, 30 m, 36 m

Construct a triangle for the given side lengths.

9. 2 in, 2 in, 3 in 11. 7 cm, 3 cm, 5 cm

25 m, 17 m, 21 m

15 cm, 22 cm, 6 cm

9 cm, 12 cm, 2 cm 8. 3 in, 17 in, 13 in

2 in, 3 in, 4 in

10 cm, 4 cm, 9 cm

Cheryl hikes a triangular trail loop. Two segments of the trail measure 4 miles and 9 miles. Can the last segment of the trail be 10 miles long for this to be a closed triangular loop?

Stan constructs a tent frame using three metal rods. He has already cut two rods: one is 5 feet long, and the other is 7 feet long. Can he use a third rod that is 2 feet long?

Billy puts a fence around a triangular garden. He has two fence pieces measuring 7 feet and 11 feet. Can the third side be 10 feet long?

A carpenter designs a triangular wooden shelf. The sides of the triangle measure 10 inches and 18 inches. Could the third side be 6 inches long?

Lesson instructions 7

Construct a triangle given the information.

Construct a triangle with a 10 cm side, 8 cm side, and a 45º angle.

1. Measure and draw one side.

2. Measure and draw the angle.

3. Measure and draw the other side.

4. Connect both sides with a line.

Construct each triangle given the information.

1. Construct a triangle with a 3 cm side, 5 cm side, and a 70° angle.

2. Construct a triangle with a 30° angle, a 60° angle, and a 6 cm side.

3. Construct a triangle with a 50° angle, a 40° angle, and a 7 cm side.

4. Construct a triangle with a 4 cm side, 3 cm side, and a 90° angle.

5. Construct a triangle with an 2 cm side, 4 cm side, and a 45° angle.

6. Construct a triangle with a 40° angle, a 70° angle, and a 6 cm side.

Lena designs a garden in the shape of a triangle. She wants two sides of the garden to be 6 meters and 3 meters long. The angle between them is 45°. Sketch what the triangular garden would look like using centimeters for meters.

A kite manufacturer is designing a triangular kite frame. Two sides of the kite are 2 feet, and the angle between them is 60°. Sketch what the triangular kite would look like using inches for feet.

A tent is being constructed, and the design requires the base of the tent to be 5 meters long. The two angles adjacent to the base are 40° and 50°. Sketch what the tent would look like using centimeters for meters.

An engineer is designing a triangular roof with a base length of 4 feet. The angles formed by the base and the sides of the roof are 35° and 65°. Sketch what the roof would look like using centimeters for feet.

Lesson instructions

Write and draw the shape that is made when the threedimensional figure is sliced.

1. Name the shape of the cross section. Pentagon

2. Draw the shape.

Write and draw the shape that is made when the three-dimensional figure is sliced.

Dan cuts a cucumber for his salad. The cucumber is shaped like a cylinder.

A. If Dan makes a straight, horizontal cut along the length of the cucumber, what shape will the cross-section be?

B. If Dan makes a straight, vertical cut through the cucumber, what shape will the cross-section be?

A factory produces boxes in the shape of cubes.

A. If a worker slices one of the boxes parallel to the base, what shape will the cross-section be?

B. If the worker slices it vertically what shape will the cross-section be?

A watermelon is shaped like a sphere.

A. If you slice it straight down the middle, what shape will the crosssection be?

B. What shape will the cross-section be if you cut it at a slight angle?

Jacob has an ice cream cone.

A. If he slices it horizontally across the top, just below the scoop of ice cream, what shape is the cross-section?

B. If he slices the cone vertically down the middle, what shape does he get?

Lesson instructions 9

Determine the radius or diameter. Find the measure of the angle.

To find the radius, divide the diameter by 2. 14 ÷ 2 = 7 radius = 7 m

The marked angle is a straight line along the diameter, therefore it is 180°.

m

Write the most specific word to describe each line that is shown: radius, diameter, or chord.

Determine the unknown radius or diameter.

Determine the unknown radius or diameter.

11. radius = 28 m diameter = 13. radius = 42.5 ft diameter = 15. radius = 16.8 cm diameter = 12. diameter = 50 in radius = 14. diameter = 55 in radius = 16. diameter = 65.2 in radius =

Use a protractor to measure the angle created by the intersecting radii.

A new park field has a center circle. The radius of the center circle is 6 yards.

A. What is the diameter of the circle?

B. If the park doubles the radius of the center circle, what would the new diameter be?

A Ferris wheel at an amusement park has a diameter of 80 feet.

A. What is the radius of the Ferris wheel?

B. If the radius were increased by 10 feet, what would the new diameter be?

A circular cake is cut into quarters.

A. What is the measure of the central angle which represents each slice of cake?

B. If each slice gets cut in half, what is the measure of each angle now?

A large round pizza is divided into 10 equal slices.

A. What is the measure of each central angle that represents one slice?

B. If someone eats 3 slices, what is the total angle of the missing part?

Lesson instructions 10

Find the circumference of each circle.

1. Determine which formula to use: C = 2πr or C = πd

2. Substitute 3.14 for pi. C = 2(3.14)(4)

3. Multiply. 25.12 m

Find the circumference of each circle.

Find the radius of each circle given the circumference.

Find the diameter of each circle given the circumference.

m

A homeowner has a circular swimming pool with a diameter of 24 feet. He wants to install a safety fence around the entire pool. How many feet of fencing will he need?

A large pizza has a radius of 7 inches. The chef wants to add a stuffed crust all the way around the edge. How many inches of stuffed crust will there be?

A circular sign has a circumference of 18.84 ft. What is the diameter of the sign?

The lid of a jar has a circumference of 12.56 in. What is the radius of the lid?

Lesson instructions 11

Find the area of each circle.

Find the area of each circle.

1. Substitute values into the area formula. A = πr2 A = (3.14)(3)2

2. Follow the order of operations. A = (3.14)(9) A = 28.26 m2

The wheel of a bicycle has a radius of 13 inches. What is the area of the wheel in square inches?

A circular window has a radius of 2 feet. How many square feet of glass will be needed to fill the window?

A circular playground has a radius of 15 meters. How much area does the playground cover?

A circular rug has a diameter of 10 feet. How many square feet of space does the rug cover?

For each set of shapes, find the scale ratio, scale factor and the missing side.

1. Divide to find the scale ratio and scale factor: 8 ÷ 4 = 2

2. Scale Ratio: 2:1

3. Scale Factor: 1 2

4. Multiply or divide to find the missing side: 12 × 1 2 = 6 m

Scale

Tell whether each set of side lengths can make a triangle. Justify your answer.

6 in, 2 in, 3 in.

1. Add each pair of sides to see if each sum is longer than the third side: 6 + 3 > 2; 6 + 2 > 3; 3 + 2 < 6

No, they cannot make a triangle.

Find the circumference and area of each circle.

radius = 3 m

1. Use C = 2πr to find the circumference.

2(3.14)(3) = 6(3.14) = 18.84 m

2. Use A = πr2 to find the area. 3.14(32) =28.26 m2

Write and solve an equation to find the missing angle measure.

1. Use angle relationships to write an equation. 5x + 105 = 180

2. Solve for the variable. x = 15

3. Substitute the value to find the missing angle measure. 15 × 5 = 75º

A cylindrical log is cut in half to create two new logs.

A sculptor has a rectangular prism of clay and slices it at an angle.

A. What shape is the cross-section?

A. What are some possible shapes the cross-section could be?

B. If one of the new logs was split in half to create two long pieces of wood, what shape would the cross section be?

B. How would the cross-section change if the sculptor sliced straight down instead of at an angle?

A rectangular pool is shown below. If the image is scaled by a scale factor of 1 2 , draw the new shape.

Scale the shape below by a scale factor of 3.

Chapter 8

In Chapter 8, we will expand on

Area and Volume

Geometric shapes can be found everywhere we look. Knowing how to calculate area and volume can help us understand the space around us.

• We will find the area of parallelograms, triangles, trapezoids, and compound figures.

• We will find the volume of rectangular and triangular prisms.

• We will find the surface area of rectangular and triangular prisms.

• We will solve real-world problems involving twodimensional and three-dimensional shapes.

Find the area of the parallelogram.

Substitute values into the area formula. A = bh A = (10)(6) A = 60 m2

Find the area of each parallelogram.

Find the missing dimension in each parallelogram.

A billboard is shaped like a parallelogram with a base of 40 feet and a height of 15 feet.

A. What is the total area of the billboard?

A large kite is shaped like a parallelogram with a base of 60 cm and a height of 35 cm.

A. How much fabric is needed to make the kite?

B. If the cost of advertising is $3 per square foot, what is the total cost to rent the entire billboard?

B. If the fabric costs $0.50 per square cm, what is the total cost?

A parallelogram-shaped picnic blanket has an area of 200 square feet and a height of 10 feet. What is the length of the base of the blanket?

A window in the shape of a parallelogram has an area of 300 square inches. The height of the window is unknown, but the base is 25 inches. What is the height of the window?

Lesson instructions 2 Find the area.

Find the area of each triangle.

Find the area of each trapezoid.

1. Substitute values into the area formula. 1 2 bh = 1 2 (10)(7)

2. Solve. 1 2 (10)(7) = 35 in2 Area of a triangle: 1 2 bh

Find the missing dimension in each shape. 9. Area = 90 m2

13. Debra found the area of the trapezoid below. Do you agree with her solution? Justify your answer.

A contractor builds a walkway in the shape of a trapezoid. The walkway has a shorter base of 6 feet, a longer base of 10 feet, and a height of 4 feet. What is the area of the walkway?

A camp manager paints a triangular section on the field. The base of the triangle is 12 meters, and the height is 7 meters. What is the area of the triangular section?

A triangular flag has an area of 52 square inches and a base of 13 inches. What is the height of the flag?

A builder installs a trapezoidal section of a roof. The top side is 6 feet, the bottom side is 14 feet, and the height is 5 feet. What is the area of the roof section?

Lesson instructions 3

Find the area of the compound shape.

1. Identify each shape. 2 rectangles

2. Find the area of each shape. 1: (12)(4) = 48 2: (3)(5) = 15

3. Add the areas of each shape together. 48 + 15 =

Find the area of each compound shape.

A garden is designed with a rectangular lawn and a square flower bed attached to one of its sides. The rectangular lawn is 15 feet long and 10 feet wide. The square flower bed has a side length of 6 feet. What is the total area of the garden?

A clock design is shaped like a triangle with a semicircle on top. The triangular base is 12 inches wide and 12 inches tall. The semicircle has a diameter equal to the base of the triangle. What is the total area of the clock face?

Joe wants to build a garden in the shape of a house, and needs to put down garden lining to keep the weeds out. How many square feet of garden lining will he need for his garden? Round your answer to the nearest hundredth.

A stage consists of a rectangular main section that is 24 feet long and 16 feet wide, with a semicircular extension at the front. The semicircle has a diameter equal to the width of the rectangle. What is the area of the stage?

Lesson instructions 4

Find the volume.

V = BH

Multiply the area of the base times the height of the figure

1. Substitute values into the volume formula.

V = BH = (10)(5)(8)

Multiply.

Find the volume of each rectangular prism.

Find the volume of each triangular prism.

Find the volume of each prism.

Find the missing dimension of each shape given the volume.

A shipping company packs boxes in the shape of rectangular prisms. Each box has a length of 15 inches, a width of 10 inches, and a height of 8 inches. What’s the volume of one box?

A builder needs to fill a triangularprism-shaped attic with insulation. The attic has a triangular base with a base that is 16 feet wide and a height that is 10 feet tall. The attic is 30 feet long. What is the volume of the attic?

Each tent has a triangular base with a base of 5 feet, a height of 4 feet, and a length of 10 feet. What’s the volume of one tent?

A bookshelf is shaped like a rectangular prism and has dimensions 48 inches wide, 12 inches deep, and 60 inches tall. What’s the volume of the bookshelf?

Lesson instructions 5

Find the surface area.

1. Find the area of the faces. S = 2(10 × 5) + 2(10 × 8) + 2(5 × 8) S = 100 + 160 + 80

2. Add the area of each face together. S = 340

Find the surface area of each rectangular prism.

Find the surface area of each triangular prism.

A cereal box has a length of 10 inches, a width of 3 inches, and a height of 14 inches. What is the total surface area of the cereal box?

A canvas tent is in the shape of a triangular prism. The triangular faces have a base of 6 feet and a height of 4 feet. The length of the tent is 10 feet, and the three rectangular faces measure 10 feet by 6 feet, 10 feet by 5 feet, and 10 feet by 7.2 feet. How many square feet of canvas is the tent made of, including the floor?

A shoe box measures 14 inches in length, 6 inches in width, and 5 inches in height. What is the total surface area of the shoe box?

A block of cheese is shaped like a triangular prism. The triangular faces have a base of 5 inches and a height of 3 inches. The length of the cheese wedge is 8 inches, and the three rectangular faces measure 8 inches by 5 inches, 8 inches by 4 inches, and 8 inches by 6.4 inches. What is the total surface area of the cheese block?

Lesson instructions 6

Find the volume and surface area.

Mike’s mattress is a rectangular prism. It has dimensions of 13 ft × 6 ft × 4 ft.

a. What is the volume? V = lwh = (13)(6)(4) = 312 ft3

b. What is the surface area? S = 2(lw + lh + wh) = 2[78 + 52 + 24] = 308 ft2

Sketch each shape described, then solve.

1. A refrigerator has an internal storage space shaped like a rectangular prism with dimensions of 36 inches by 30 inches by 72 inches. What is its total volume in cubic inches?

2. A slide is in the shape of a triangular prism. The base of the triangle is 5 feet, the height is 3 feet, and the length of the slide is 12 feet. What is the volume of the slide’s interior space?

3. A gift box is shaped like a triangular prism whose base has an area of 10 cm2. The box is 20 cm long. The sides of the triangle have lengths of 7 cm, 9 cm, and 4 cm. What is the total surface area of the box?

4. A rectangular prism-shaped sand storage bin has a length of 15 feet, a width of 8 feet, and a height of 4 feet. What is the surface area of the box?

A rectangular prism-shaped shed is being built with dimensions 12 feet long, 8 feet wide, and 10 feet high.

A. What is the volume of the shed?

A fish tank is in the shape of a rectangular prism with dimensions 30 inches long, 12 inches wide, and 18 inches high.

A. What is the volume of water the aquarium can hold in cubic inches?

B. If all the walls, the roof, and the floor need to be painted, what is the total surface area to be painted?

B. If the top is open, what is the total surface area of the glass panels used to build the tank?

A barn has a roof in the shape of a triangular prism. The triangular crosssection has a base of 12 feet and a height of 5 feet, and the roof extends for 30 feet.

What is the total volume of the space under the roof?

A sled is designed in the shape of a triangular prism. The equilateral triangular front has a base of 15 inches and a height of 13 inches, while the sled is 48 inches long.

A. What is the total volume of the sled?

B. What is the surface area of the sled?

Find the area of each shape.

Area of a parallelogram: A = bh

Area of a triangle: A = 1 2 bh

Area of a trapezoid: (b₁ + b₂) 2 × h

Find the area of each compound figure. Round to the nearest hundredth if necessary.

1. Identify each shape. 2 rectangles

2. Find the area of each shape. 1: (9)(5) = 45 2: (4)(5) = 20

3. Add the areas of each shape together.

45 + 20 = 65 m2

Find the volume and surface area of each prism. Round to the nearest hundredth if necessary.

1. Substitute values into the volume formula and solve.

V = Bh = (9)(4)(8) = 288 in3

2. Find the area of each face and add them all up to find the surface area. S = 2[(9)(4)] + 2[(9)(8)] + 2[(4)(8)] S = 280 in2

A house has a rectangular main living area measuring 50 feet by 30 feet.

Attached to one side is a triangular front porch with a base of 30 feet and a height of 10 feet. What is the total area of the floor, including the porch?

An ice skating rink consists of a rectangular rink that is 60 feet long and 40 feet wide. Surrounding it on both shorter sides are two identical semicircular seating areas, each with a radius of 20 feet. What is the total area of the rink and seating areas combined?

A rectangular pencil case has a length of 12 inches, a width of 6 inches, and a height of 2 inches.

A. What is the volume of the pencil case?

A vase is in the shape of a triangular prism. The equilateral triangular base has side measurements of 14 inches and a height that measures 12 inches. The height of the vase is 17 inches.

A. What is the volume of the vase?

B. What is the surface area of the pencil case?

B. What is the surface area of the vase?

Chapter 9

In Chapter 9, we will expand on

Statistics and Data Analysis

Statistics and data analysis help us make sense of information in the world, recognize patterns, and help inform our decisions based on evidence rather than guesswork.

• We will identify populations and samples.

• We will determine if a sample is biased.

• We will calculate and interpret measures of center in data.

• We will model and interpret the spread of data using box plots and dot plots.

• We will write inferences about a population based on the data from a sample.

Identify populations and samples.

Population → Students in a School Sample → 25 Students from Each Grade

Population → People in a Town Sample → 100 Random Residents

Determine the population and the sample.

1. A clothing store surveys 130 customers about their favorite clothing brands.

2. A teacher selects 30 students from different grade levels to test a new math curriculum.

3. A restaurant asks 300 customers about their satisfaction with a new menu item.

Population:

Sample:

Population:

Sample:

Population:

Sample:

Evaluate if the sample is biased or unbiased. Explain your reasoning.

4. A zoo wants to improve visitor satisfaction. They survey 500 people who visited on a rainy weekday in the winter.

Match the sample to the population it best represents.

5. 1,200 voters randomly selected across all 50 states to predict election results.

6. 500 students randomly chosen from 10 different middle schools across a state.

7. 300 residents surveyed from different neighborhoods in a large city to evaluate public transportation.

8. 100 students from different 7th-grade classes surveyed about their homework load.

9. 150 teachers randomly selected from different schools in a school district.

A. All middle school students in the state

B. All teachers in the school district

C. All 7th-grade students in a school

D. All voters in the country

E. All residents of the city

A city government wants to see what people think about road conditions. They randomly select 700 residents from various neighborhoods in the city.

Population: Sample:

Is the sample biased? Why or why not?

A high school wants to determine if students get enough sleep. They survey only students in the school’s morning classes.

Population: Sample:

Is the sample biased? Why or why not?

A town government wants to know how often residents use public parks. They survey people who are visiting a park on a Sunday afternoon.

Population: Sample:

Is the sample biased? Why or why not?

A men's suit store wants feedback on customer service. They randomly select 1,000 shoppers from multiple store locations.

Population: Sample:

Is the sample biased? Why or why not?

Lesson instructions 2 Make inferences about the population based on the samples.

Population: All the batteries are made by Better Batteries. The mean lifespan of a random sample of 10 batteries is 52 hours.

Inference: The average lifespan of all the batteries made by Better Batteries is likely 52 hours.

Find the mean, median, and mode of the data set. Then, for each statement circle true or false.

A math teacher recorded the scores on a recent 10-point quiz of a random sample of 8 students in 7th grade.

Data Points: 7, 7, 8, 8, 8, 9, 10, 10

Mean:

Median:

Mode:

1. At least half of the students in the sample scored 8 or lower.

2. It is likely that if all of the students in the grade took the quiz, most would score an 8.

3. It is likely that if all of the students in the grade took the quiz, only one student would score a 9.

4. If all students in the grade took the quiz, the average score would be exactly 8.375.

5. If all students in the grade took the quiz, they would all score an 8.

A school counselor is investigating the time students spend on homework (in minutes) each night and surveys three random groups of 10 students.

Group A: 20, 25, 30, 30, 35, 35, 40, 45, 50, 60

Group B: 30, 35, 35, 40, 40, 45, 45, 50, 50, 55

Group C: 10, 20, 30, 35, 40, 40, 45, 50, 55, 60

A. What is the median time spent on homework (in minutes) for each group?

B. Should Sample A be used alone to predict the median homework time for all students? Why or why not?

A teacher records the time (in minutes) it takes three random groups of 9 students to complete a test.

Group A: 15, 16, 17, 18, 19, 20, 21, 22, 23

Group B: 17, 18, 19, 20, 21, 22, 23, 24, 25

Group C: 28, 29, 30, 31, 32, 33, 34, 35, 36

A. What is the median completion time for each group?

B. The teacher concludes the typical test completion time is 32 minutes. Is this a good inference?

A survey asks three random groups of 8 adults how many books they read last year.

Group R: 5, 6, 7, 8, 8, 10, 11, 11

Group S: 0, 2, 4, 6, 6, 7, 9, 11

Group T: 2, 4, 4, 9, 9, 11, 11, 13

A. What is the mean number of books read for each group?

B. Is it more likely the population average is near 5 books or near 8 books?

A call center monitors the number of calls received during 5 random 1-hour periods. They use 3 samples.

Sample 1: 45, 46, 47, 48, 49

Sample 2: 45, 45, 46, 47, 48

Sample 3: 39, 40, 45, 45, 46

A. What is the mean number of calls for each period?

B. What would be a good estimate for the average number of calls per hour for the call center?

Lesson instructions 3 Compare the spread and variability in data sets with visual representations.

Number of Chestnuts Collected Number of pages in each book

Use the graphs to answer questions 1-4.

A sample of the math test scores for two class periods were plotted in the dot plots to show the distribution of scores.

Which class has a higher center? How do you know?

In which class did students vary more in their scores? How do you know?

Which class did better in general on the test? How do you know?

In which class are students' scores more predictable? How do you know?

Lesson instructions 4

Find the range, IQR, and MAD.

Interquartile Range:

1, 2, 2, 7, 8, 10

Third Quartile - First Quartile IQR: 8 - 2 = 6 Range

Maximum - Minimum 10 - 1 = 9 MAD

Mean of the Differences from the Mean

Find the range of each data set.

11, 8, 5, 4, 6, 14

Find the MAD of each data set.

15. 6, 9, 12, 15, 18, 21 18. 10, 12, 14, 16, 18, 20

5, 7, 9, 11, 13 19. 30, 35, 40, 45, 50, 55 17. 4, 8, 12, 16, 20, 24 20. 23, 11, 14, 20, 17 5

Find the range, IQR, and MAD of each data set.

21. 10, 15, 20, 25, 30, 35 Range: IQR: MAD: 22. 5, 7, 9, 11, 13, 15 Range: IQR: MAD: 23. 6, 9, 12, 14, 17, 20 Range: IQR: MAD: 5. 11, 15, 16, 19, 20 6. 2, 42, 85, 23, 25, 18

Find the IQR of each data set. 8. 10. 9. 11. 12. 5, 15, 25, 35, 45 13. 62, 58, 74, 95, 23, 17

14. 2, 2, 6, 9, 5, 4, 2, 9

A teacher records the number of minutes 12 students spend studying each day over a two-week period. The following data represents the study times (in minutes) for each student:

30, 45, 50, 60, 55, 70, 80, 65, 90, 85, 75, 100

What is the range of time spent studying?

A bookstore is reviewing the number of books sold per day over the past 14 days. The following data represents the daily sales (in books):

10, 12, 15, 18, 20, 22, 25, 28, 30, 32, 35, 38, 40, 45

What is the IQR of the daily sales?

A bakery tallies the number of pastries sold each day over the course of a week. The following data represents the daily sales (in pastries):

20, 22, 24, 26, 28, 30

To find how much each day’s sales varies from the mean, find the Mean Absolute Deviation (MAD) and write if there is a lot of variation or a little.

A restaurant tracks the number of meals served each day over the course of a week. The following data represents the daily meals served (in meals):

100, 110, 120, 130, 140, 150

To find how much variation from the mean there is each day, find the Mean Absolute Deviation (MAD).

Lesson instructions 5 Use measures of centers and measures of variability from samples to compare two populations.

Sample 1:

Students who walk

Mean: 10 minutes

Measures of Center

Measures of Variability

Median: 5 minutes Mode: 5 minutes

Range: 29 IQR: 9 MAD: 8

Sample 2:

Students who drive

Mean: 12 minutes

Median: 11.5 minutes Mode: 13 minutes

Range: 20 IQR: 5 MAD: 5.3

Inferences:

Generally, students who walk to school travel for a shorter amount of time than students who drive.

Generally, students who walk to school have greater variability in the times they spend traveling than students who drive.

A farmer has two orchards. He wants to compare the number of apples per tree in each orchard. He selects a random sample of 20 trees from each orchard and marks the numbers of apples.

The results are in the tables below. Write likely or not likely for each inference about the whole population.

1. The average number of apples per tree in Orchard B is lower than Orchard A.

2. All the trees in Orchard A have more apples than Orchard B.

3. The median number of apples per tree in Orchard A is greater than in Orchard B.

4. Orchard B has more variation in the number of apples per tree than Orchard A.

5. Orchard B has more consistency in the number of apples per tree compared to Orchard A.

6. The difference between the tree with most apples and the tree with the least apples is larger in Orchard A than Orchard B.

Two car dealerships want to know which dealership charges more in general. They each take random sample of 10 cars to track.

Dealership A:

$15,000, $18,000, $20,000, $22,000, $25,000, $30,000, $35,000, $40,000, $42,000, $50,000

Dealership B:

$13,000, $15,500, $17,000, $18,500, $22,000, $25,000, $28,000, $30,000, $35,000, $40,000

What is the mean in each sample?

Make an inference comparing average price of cars from Dealership A and B.

A farm tracks the number of eggs laid by brown hens and black hens each day. The following data represents the daily egg count of 10 random hens from each group:

Brown hens:

5, 6, 7, 8, 9, 10, 13, 15, 17, 18

Black hens:

6, 8, 10, 12, 15, 18, 20, 25, 28, 30

Find the IQR for both samples:

Make an inference comparing the variability in the amount of eggs from all the black and brown hens.

A bakery wants to know if they sell more pastries on Mondays or Fridays. The following data represents the daily pastry sales for a random 7 Mondays and 7 Fridays:

Mondays:

50, 60, 70, 80, 90, 100, 110 Fridays: 55, 65, 75, 85, 95, 105, 140

What is the range of pastries sold in the samples from Mondays and Fridays?

Does this mean that the number of pastries sold on all Fridays are less consistent than the number sold on Mondays?

Two schools want to compare the final exam scores of their students. The following data represents the test scores for a random sample from each school:

School 1:

100, 70, 95, 90, 95, 100, 80, 95 School 2: 85, 100, 100, 95, 100, 90, 80

What is the mode for both samples?

Does that mean that the most common score of all the students in School 2 was higher than the most common score from School 1? Explain.

Identify the population and the sample.

Population → All the Candy in a Bag

Sample → 25 Randomly Selected Pieces of Candy

1. A pet store wants to know the most popular hamster toy is. They survey 200 hamster owners.

Population:

Sample:

State if the sample is biased or unbiased.

2. To find out if students enjoy reading, a librarian surveys only students who are checking out books.

Biased Sample Unbiased Sample

3. A school counselor randomly selects 50 students from the entire middle school to ask about their favorite school subject.

Find the mean, median, and mode.

3, 5, 7, 9, 11

Mean

Sum of the values:

4 + 4 + 6 + 7 + 14 = 35

Divided by total:

35 ÷ 5 = 7 → Average = 7

Median

4, 4, 6, 7, 14

Middle number = 6

Mode

4, 4, 6, 7, 14

Most common number = 4

Find the range, IQR, and MAD.

8. 3, 5, 7, 9, 11

Interquartile Range:

Third Quartile - First Quartile

Range

Maximum - Minimum

MAD

Mean of the Differences from Mean

9. 4, 4, 6, 8, 10, 12, 14

10. 1, 2, 2, 3, 3, 4, 4

11. 10, 12, 12, 13, 14, 14, 16

Mean: Median: Mode:

Mode:

Range: IQR: MAD:

Range: IQR: MAD:

Range: IQR: MAD:

Range: IQR: MAD:

To find out how many students in school enjoy art class, a teacher asks every student currently enrolled in an art class.

A. What is the population?

B. Is the sample biased or unbiased? Explain.

A. Which graph has a greater center?

B. Which graph has a greater spread?

A store manager monitors the time (in minutes) it takes two employees to stock a shelf. They record the times for 5 random instances for each employee.

Employee A: 8, 9, 10, 11, 12

Employee B: 5, 8, 10, 12, 15

Which employee is likely more consistent in their stocking time, as shown by the range? Explain.

A school tracked the number of volunteer hours completed by a random sample of 10 students from 7th grade and 10 students from 8th grade.

7th Grade: 20, 25, 30, 30, 35, 40, 40, 45, 50, 55 8th Grade: 15, 20, 25, 30, 35, 40, 50, 60, 65, 70

A. Find the mean number of hours for 7th and 8th graders.

B. Make an inference comparing the typical number of volunteer hours completed by all 7th and 8th graders.

Chapter 10

In Chapter 10, we will expand on

Probability

Probability helps you predict how likely something is to happen so that you can plan ahead better.

• We will use data to write probabilities and predict outcomes.

• We will compare theoretical and experimental probabilities.

• We will calculate probabilities for compound events.

• We will identify sample spaces and calculate possible outcomes.

• We will analyze simulations to help visualize larger scale events.

State the likelihood of each event.

State the likelihood of each event.

1. The probability of picking one of the 21 consonants out of a bag with 26 letter tiles.

3. The probability of snow falling in July in a tropical country is 0%.

There is a 20% chance that there will be a test today. It is unlikely that there will be a test today. impossible

2. A game spinner has 10 equal sections: 3 red, 4 blue, and 3 green. The probability of landing on blue or red is 70%.

4. The probability of getting at least one heads is 0.75, when flipping two coins.

Change the probability to change the event’s likelihood. Tell what the new likelihood is.

5. The chance of snow tomorrow is 30%.

6. The chance that a 7th grader will bring a water bottle to school is 5 6 .

7. The chance of randomly picking a blue marble from a bag is 0.3.

8. A student has a 10% chance of being called on in class.

9. The chance of pulling a red jellybean from the jar is 0.7.

10. The probability of a store selling out of a popular item is 0.8.

11. A swimmer has a 2 5 chance of beating their personal record in a race.

12. The probability of getting a question correct on a multiple-choice test is 0.25.

13. The weather forecast predicts a 9 10 chance of sunshine.

1

Liam has four socks in a drawer. Two are white, one is black, and one is red. If he randomly picks one sock, what is the likelihood that he picks:

A. A white sock?

B. A black sock?

C. A red sock?

D. A blue sock?

In a game of chance, the probability of selecting a blue marble is given as 0.78. What is the likelihood of this event occurring?

A bag contains a total of 4 cards: 1 with a star and 3 with a circle. The probability of picking a card with a circle is 0.75. What is the likelihood of this event occurring?

The chance of it raining today is likely. The weather report changes, and the chance of rain is now 25%. What is the new likelihood of it raining?

Lesson instructions 2

Find the probability, and make a prediction.

A fisherman catches 6 fish out of ten 10 tries. Find the experimental probability. Predict how many catches he would make out of 80 tries.

a. P = # of events # of trials = 6 10 = 3 5 = 0.6 = 60% b. 3 5 = x 80 x = 48

Find the experimental probability given the data. Write it as a fraction, decimal, and percent.

4. A deck contains 30 cards: 10 red, 8 blue, and 12 green. Jamie randomly picks a card, records the color, and replaces it before picking again. After 90 trials, she picked a red card 27 times. What is P(red)?

5. Fred played a game 60 times and won 48 times. What is the experimental probability that he wins a game?

Make predictions using the probability.

6. A baker made 120 cookies in 2 hours. Predict how many cookies they will make in 5 hours?

7. A student correctly answered 15 out of 20 questions on a practice test. If the actual test has 80 questions, predict how many questions would they answer correctly?

8. Emily read 12 books in the first 3 months of the year. Predict how many books she will read in 12 months?

9. A farm worker picked 45 apples in 15 minutes. Predict how many apples he will pick in one hour.

Emma flipped a coin 120 times and landed on heads 52 times.

A. What is the experimental probability of flipping heads?

A jar contains different colored candies. Sophia randomly picked a candy, recorded its color, and put it back. After 100 trials, she picked a red candy 37 times.

A. What is the experimental probability of picking a red candy?

B. If she flips the coin 300 times, how many times should she expect to land on heads?

B. If she picks a candy 500 times, how many times should she expect to get red?

A game wheel is divided into four equal sections: red, blue, green, and yellow. Jackson spun the wheel 90 times and landed on green 28 times.

A. What is the experimental probability of landing on green?

Liam got the ball into the basket 45 out 80 tries.

A. What is the experimental probability that Liam gets the ball in?

B. If he spins the wheel 250 times, how many times should he expect to land on green? Round your answer to the nearest whole number.

B. If he shoots 240 times, how many should he expect to make?

Lesson instructions 3

Find the theoretical and experimental probability. Leslie flipped a fair coin. The results are shown below: Heads: 12 Coins: 8

1. What is the theoretical probability of landing on heads?

P(H) = 1 2 = 0.5 = 50%

2. What is the experimental probability of landing on heads?

P(H) = 3 5 = 0.6 = 60%

Write the theoretical probability as a fraction, decimal, and percent.

1. What is the probability of rolling an odd number on a six-sided die?

2. A bag contains 6 red marbles, 5 pink marbles, and 4 yellow marbles. What is the probability of pulling a red marble? Red: 3 Blue: 5 Yellow: 4

3. Jenny has a bag of marbles. The bag contains 6 red marbles, 9 blue marbles, and 5 yellow marbles. She pulled 12 marbles from the bag. The results are shown below:

A. What is the theoretical probability of pulling each color of marble?

B. What is the experimental probability of pulling each color based on the results?

C. Compare the theoretical and experimental probabilities for each color. Are they the same or different? Explain why this might happen.

Emma has a basket with 40 pieces of fruit: 16 apples, 10 bananas, and 14 oranges.

What is the theoretical probability of selecting each type of fruit?

Emma randomly selects 20 pieces of fruit. The results are shown below:

Apples: 10

Bananas: 4

Oranges: 6

What is the experimental probability of selecting each type of fruit based on the results?

Compare the theoretical and experimental probabilities of picking each fruit.

Why might the experimental probability be different from the theoretical probability. What can Emma do to try and make the probabilities closer.

Lesson instructions 4

Find the sample space.

Rosie rolls two, six-sided dice. How many possible outcomes are there? 6 × 6 = 36 outcomes

Find the number of outcomes.

1. A library has 9 different genres of books, and each genre has 7 books available. How many total books can a person choose from?

3. A toy store sells 6 types of dolls and each comes with 3 different outfits. How many different doll-and-outfit combinations are available?

2. A school vending machine offers 10 different drinks and 4 types of snacks. How many different drink-and-snack combinations can a student buy?

4. A new restaurant allows customers to create a custom sandwich by choosing from 2 types of buns, 5 types of proteins, and 4 types of vegetables. How many unique sandwiches can be made?

Organize and answer questions about the sample space by creating a tree diagram or table.

5. Mark is packing for a trip. He can bring a red, blue, or black jacket; cap or visor; and sneakers or boots. How many possible outcomes are there?

6. Noah is choosing a school lunch. He can have a sandwich (Deli, Tuna, or PB&J) and a side (Chips or Fruit). How many outcomes are there?

A restaurant offers a meal deal. Customers choose a main dish (pasta, pizza, or salad), a side (fries, onion rings, or fruit salad), and a drink (soda, lemonade, or water). How many possible combinations are there?

Emma is decorating her room. She must choose a wall color (pink, blue, yellow, or white), a lamp style (modern or vintage), and a bedspread design (stripes, floral, or solid). How many possible combinations are there?

James is customizing his bike. He picks a frame color (red, blue, green, or black), a wheel color (white, black, or neon), and a sticker design (polka dots, flames, or lightning). How many combinations are there?

Lily is ordering an ice cream sundae. She can pick an ice cream flavor (chocolate, vanilla, strawberry, or mint), a topping (sprinkles, nuts, cherries, or whipped cream), and a syrup (caramel or chocolate). How many combinations are there?

Lesson instructions 5

Find the compound probability.

Ronnie flips a coin and rolls a 6-sided die. What is the probability of landing on tails and rolling a 2 or 3?

1. Find each probability.

2. Multiply the probabilities. P(Tails) = 1

3) = 1 3

Find the compound probability. Write your answer as a fraction, decimal, and percent.

1. A spinner has 5 equal sections labeled A, B, C, D, and E. A six-sided die is rolled. What is the probability of spinning a B and rolling a 5?

2. A fair coin is flipped, and a tensided die (1-10) is rolled. What is the probability of flipping heads and rolling a number greater than 7?

3. A bag contains 4 red, 5 blue, and 3 green marbles. A four-section spinner (1, 2, 3, 4) is spun. What is the probability of drawing a blue marble and spinning a 1 or 3?

4. A spinner has 8 equal sections numbered 1-8, and a fair coin is flipped. What is the probability of spinning a number less than 5 and flipping tails?

5. Two six-sided dice are rolled. What is the probability of rolling a 2 on the first die and a number greater than 4 on the second die?

5. A bag contains 7 yellow, 5 blue, and 6 red marbles. A six-sided die is rolled. What is the probability of drawing a yellow marble and rolling an even number?

7. A number is randomly chosen from 1 to 20, and a six-sided die is rolled. What is the probability of selecting a multiple of 5 and rolling an odd number?

8. A four-sided die (1-4) is rolled, and a fair coin is flipped. What is the probability of rolling a 3 or 4 and flipping heads?

Leo, Max, and Ethan are playing a board game. The game involves rolling a sixsided die and drawing a card from a deck of 20 special cards (5 red, 6 blue, 4 green, and 5 yellow).

To win a bonus turn, a player must:

1. Roll an even number on the die.

2. Draw a blue or yellow card from the deck.

What is the probability that Leo wins a bonus turn on his first try?

A school is holding a fundraiser where students randomly pick a raffle ticket from a box and spin a four-section spinner (labeled A, B, C, and D).

The rules for winning the grand prize are:

1. Drawing a ticket number ending in 3 or 7 (out of 100 total tickets).

2. Spinning either A or B on the spinner.

What is the probability that a student wins the grand prize?

At a carnival, there is a booth where players must roll two six sided dice and get a sum higher than 8 in order to win.

What is the probability of a player winning the prize?

At a school science fair, a student runs a probability experiment where participants must:

1. Pick a card from a deck of 40 cards, where 15 are marked "win" and 25 are marked "lose".

2. Draw a marble from a bag containing 12 marbles (4 red, 3 green, 5 blue). To win, they must draw either a green or blue marble.

What is the probability of a participant winning the science fair experiment?

Lesson instructions 6

Conduct a simulation to determine the probability.

A claw machine game has a win rate of only 5% (1 in 20). How can you simulate the probability of winning if you play 4 times?

Randomly choose four numbers from 1-20. Each time, mark a check if there is a 1 in the set of four. Mark an x if there is no 1 in the set.

Repeat 50 times.

Then, find the experimental probability of getting a check.

Answer the questions to determine the probability

1. A cereal company puts a rare "Golden Ticket" in 10% of their cereal boxes. Tim wants to know the probability that he will have to buy more than 5 boxes to find a ticket.

A. Tim uses a random number generator for integers 1 to 10. He assigns the number 1 as "Found Ticket." What do numbers 2 through 10 represent?

Tim generates numbers until he gets a 1. He counts how many numbers he had to generate. He repeats this simulation 40 times.

Number of numbers until getting a 1

B. What is the probability that Tim has to buy more than 5 boxes (6 or more) to find a ticket?

C. Is it likely that it will take more than 6 boxes to find a ticket?

2. A student forgot to study for a 10 question quiz. The quiz has multiple-choice questions with 4 possible answers (A, B, C, D). Only one answer is correct. The student wants to know the chance of guessing the correct answer on at least 4 of the questions.

A. The student uses a spinner with 4 sections. Landing in the red represents a correct answer. What do the other sections represent?

The student spins the spinner ten times and marks the number of times it landed on the red and repeats this 40 times.

Number of times a red was spun

B. What is the probability of spinning a red at least 4 times?

C. Is it likely that the student will guess at least 4 answers correctly?

Dan passes through 4 traffic lights on his way to work. Each light has a 25% chance of being red when they arrive. How can he simulate the probability of hitting 4 green lights in a row?

A. Roll a 6-sided die 4 times. If it lands on 1 all 4 times, mark a check. If it doesn’t land on 1 all 4 times, mark an x.

B. Spin a 4 sectioned (one section is red) wheel 4 times. If it lands on red all 4 times, mark a check. If it doesn’t land on red all 4 times, mark an x.

C. Flip a coin 6 times. If it lands on heads all 6 times, mark a check. If it doesn’t land on heads all 6 times, mark an x.

A weather forecast predicts a 50% chance of rain for Saturday and a 50% chance of rain for Sunday. How can you simulate the probability that it rains on just one of the days?

A. Roll a 6-sided die 2 times. If it lands on 1-3 both times, mark a check. If it lands on 4-6 any of the times, mark an x.

B. Flip a coin 2 times. If it lands on heads both times, mark a check. If it doesn’t land on heads both times, mark an x.

C. Flip a coin twice. If it lands on heads exactly one time, mark a check. If it doesn’t land on heads exactly one time, mark an x.

A factory produces lightbulbs where approximately 1 in 100 are defective. How can you simulate the probability of finding more than 5 defective light bulbs in a batch of 500 bulbs?

A. Generate a set of 500 random numbers 1-100. If the set contains more than 5 ones, mark a check. If the set contains 5 or less ones, mark an x.

B. Generate a set of 100 random numbers 1-500. If the set contains more than 5 ones, mark a check. If the set contains 5 or less ones, mark an x.

C. Generate a set of 100 random numbers 1-100. If the set contains a one, mark a check. If the set does not contain a one, mark an x.

A store is giving away scratch-off tickets. 1 in 4 tickets wins a small prize. How can you simulate the probability of winning a prize if you get 8 tickets.

A. Generate a set of 24 random numbers 1-8. If the set contains more than 4 ones, mark a check. If the set contains 4 or less ones, mark an x.

B. Generate a set of 4 random numbers 1-8. If the set contains a one, mark a check. If the set does not contain a one, mark an x.

C. Generate a set of 8 random numbers 1-4. If the set contains a one, mark a check. If the set does not contain a one, mark an x.

State the likelihood of each event.

What’s the likelihood of landing on heads when flipping a coin?

0% = impossible

1% – 49% = unlikely

50% = as likely as not

51% – 99% = likely

100% = certain

1. A spinner with 8 equal sections (4 red, 2 blue, 2 green) is spun. What is the likelihood of landing on a red section?

Make predictions using the probability.

A contest has a winner in 75 out of 300 rounds. Predict how many wins there will be after 500 rounds.

1. Determine probability: 1 4

2. Create and solve a proportion.

1 4 = x 500 x = 125

4. A student submits 50 homework assignments, and 42 receive full credit. If they submit 250 more assignments, how many should they expect to receive full credit on?

2. You randomly pick a letter from the word "MATH". What is the likelihood of picking the letter Z?

3. A fisherman catches fish 45 out of 150 tries. If he tries 600 more times, how many catches should be expected?

Answer each question. Write your answers as a fraction, decimal, and percent.

Danny flips a coin 20 times. He lands on heads 14 times.

Theoretical probability

= 1 2 = 0.5 = 50%

Experimental probability = 7 10 = 0.7 = 70%

5. A spinner has 8 equal sections numbered 1 through 8. What is the probability of landing on a number greater than 2?

6. A train arrives on time 64 out 100 times. What is the probability that it arrives on time?

Organize and answer questions about the sample space using any method.

A clothing store sells 6 types of shirts, 5 pairs of pants, and 4 different hats. How many unique outfits can be created?

6 × 5 × 4 = 120 outfits

7. A smoothie shop has 3 base flavors, 5 fruit mix-ins, and 4 toppings. How many smoothie combinations can be made?

8. A custom couch has 7 fabric color options, 3 cushion styles, and 4 leg designs. How many couch designs are possible?

Find the compound probability. Write your answer as a fraction, decimal, and percent.

A coin is flipped, and a six-sided die is rolled. What is the probability of flipping tails and rolling an even number?

1. Find each probability. P(T) = 1 2 P(even) = 1 2

2. Multiply: 1 2 × 1 2 = 1 4

9. A deck of 10 cards numbered 1-10 is shuffled, and a coin is flipped. What is the probability of drawing an even number and flipping tails?

A raffle has a 1 in 6 chance of winning a prize. 180 tickets were drawn, and 28 of them were winners.

A. What is the theoretical probability of winning?

A restaurant promotion offers a prize in 40% of their kids' meals. In a party of 150 kids meals there were 52 prizes.

A. What is the theoretical probability of getting a prize?

B. What is the experimental probability of winning?

B. What is the experimental probability of getting a prize?

A carnival ring toss game has a 1 in 8 chance of landing a ring on a bottle. A player tossed 240 rings and landed 34 successfully.

A. What is the theoretical probability of landing a ring on a bottle?

A vending machine dispenses a "Lucky Soda" once every 5 drinks on average. 200 drinks were purchased, and 47 of them were Lucky Sodas.

A. What is the theoretical probability of getting a Lucky Soda?

B. What is the experimental probability of landing a ring on a bottle?

B. What is the experimental probability of getting a Lucky Soda?

Chapter 11

In Chapter 11, we will conclude with

Review

This chapter includes all of the concepts covered in the book.

• We will review adding, subtracting, multiplying, and dividing integers and rational numbers.

• We will review how to work with expressions, equations, and inequalities.

• We will review proportional relationships and using ratios, rates, and percents.

• We will review geometry concepts such as angles, scale factors, construction, area, perimeter, volume, and surface area.

• We will review how to write inferences from data using statistics.

• We will review how to predict outcomes and likelihood using probability.

Order from least to greatest. 1.7 8 , -0.85, -0.8,4 5 ,6 7 2.

Convert to same form: 1 2 , -0.5, - 1 8 → 0.5, -0.5,

Compare values:

-0.5 < -0.125 < 0.5

Arrange in order: -0.5, - 1 8 , 0.5

Add or subtract to solve.

Same sign add:3 5 + - 1 5 =4 5

Different sign subtract: 6 7 + - 5 7 = 1 7

Convert subtraction to addition using keep, add, change:1 42 4 =1 4 + - 2 4 =3 4

Multiply or divide to solve.

Same sign → positive -0.5 × -1.2 = 0.6

Different sign → negative -0.5 × 1.2 = -0.6

Convert division to multiplication using keep, change, flip:

1 2 ÷ - 2 5 → 1 2 × - 5 2 = -1 1 4

=

=

1

Two friends, Eitan and Moses, tracked their bank balances over the weekend.

Eitan started with $120 and ended with -$30.

Moses started with $90 and ended with -$15.

Which person had the greater change in balance and by how much?

Deborah baked 4 trays of cookies with 12 cookies per tray.

She accidentally burned 10 of them. She sold the remaining cookies for $1.75 each, and she spent $9 on ingredients.

How much profit did she make?

Rachel has 6 3 4 cup of flour. She uses 2 1 4 cups of flour in each batch of cookies she makes. How many batches of cookies can she make?

Richard starts hiking down a valley. He starts at sea level and descends 1 3 4 miles. He then climbs back up 2 5 mile to a rest stop. After resting, he descends another 1 1 2 miles to the base. What is Richard's elevation now?

Translate each statement into an algebraic expression.

Twelve more than 4 times a number.

1. Interpret key words. more than = + times = × a number = x

2. Write the expression. 12 + 4x

1. Three times a number decreased by 8.

3. Seven more than twice a number 2. Half of a number plus 5. 4. The difference between a number and 3, all divided by 4.

Evaluate each expression if a = -6, b = 3 4 , and c = 2.3.

x + 4y if x = 3 and y = 5

1. Substitute the values into the expression. 2(3) + 4(5)

2. Use order of operations. 6 + 20

3. Simplify. 26

Simplify each expression.

19b - 7(12b + 6)

1. Use the distributive property to multiply. 19b - 7(12b) + (-7)(6) 19b - 84b - 42

2. Combine like terms. -65b - 42

Factor each expression.

12x + 24

1. Find the GCF (greatest common factor) 12

2. Divide both terms by the GCF. 12(x + 2)

5x + 3 − 2x + 7

3(2a + 5) − 4a + 63

2(x + 6) − 3(x − 2)

6(2a − 1) + 4(3a + 2)

2 20. 6b – 24c + 12

-64x + 16

56t + 49

50r + 30s

4y − 2(3y − 5) + 8

7(3b − 2) + 5b 16. 2(3y + 4) − 5(y − 3) 18. 3(x − 4) + 2(x + 7) − 5

-30x + 45y 24. 4j – 36k + 16

James is preparing for a picnic and needs to buy supplies. He wants to buy sandwiches, drinks, and a blanket. The cost of each sandwich is $4, each drink costs $2, and the blanket costs $20. James plans to buy x sandwiches and y drinks, and he also needs to buy one blanket. Additionally, there is a delivery fee of $6 for the entire order.

A. Write an expression to represent the total amount of money James will spend on the picnic supplies.

B. If James buys 6 sandwiches and 12 drinks, how much will he spend in total?

Emily is organizing a fundraiser for her school and is selling handmade bracelets. Each bracelet is made of beads and string. The cost of the beads is $1.50 per bracelet, and the cost of the string is $0.75 per bracelet. Emily plans to make x bracelets. In addition to the materials, she needs to spend $2 for packaging for each bracelet.

A. Write an expression to represent the total cost for making x bracelets, including the cost of beads, string, and packaging.

B. If Emily makes 10 bracelets, how much will she spend in total?

A triangle has a base of 5 inches and a height of 3h + 4 inches.

A. Write and simplify an expression to represent the area of the triangle.

B. What is the area of the triangle if h = 6?

Jack is preparing to paint his house. The cost of paint is $12 per gallon, and he needs 2.5 gallons of paint for the walls. In addition to the paint, he will need to buy brushes, which cost $6 each. Jack plans to buy y brushes.

A. Write an expression to represent the total cost for buying the paint and brushes.

B. If Jack buys 4 brushes, how much will he spend in total?

3h + 4 5 in

Solve each one-step equation. Check your solution.

x + 9 = 18

1. Use inverse operations. x + 9 = 18 - 9 - 9

2. Write the solution. x = 9

Solve each two-step equation. Check your solution.

3x + 2 = -1

1. Undo addition/subtraction. 3x + 2 = -1 - 2 - 2

2. Undo multiplication/division. 3x = -3 ÷ 3 ÷ 3

3. Write the solution. x = -1

Solve each one-step inequality. Graph your solution.

= -18

1. Use inverse operations. Flip the sign if you multiply or divide by a negative number. -3x > -18 ÷ -3 ÷ -3

2. Write and graph the solution. x < 6 -6 -7 -8 -5 -4

Solve each two-step inequality. Graph your solution.

-2x + 5 ≥ 29

1. Undo addition/subtraction. -2x + 5 ≥ 29 -5 -5

2. Undo multiplication/division. -2x > 24 ÷ -2 ÷ -2

3. Write and graph the solution. x ≤ -12

Danielle earns $15 for each crochet project she sells. She also earned a $5 tip from one of her customers. If she made $80 total, how many crochet projects did she sell?

A group of 10 friends started with a box of stickers that they split evenly. Afterwards, they each gave their sibling 3 stickers. If they each want to end up with at least 6 stickers in all, how many stickers would they need to start with?

Stan wants to save more than $300 for a new piano. He already has $90 saved and earns $20 per hour at his part-time job. Write and solve an inequality to determine how many hours he needs to work.

A hot air balloon can hold a maximum of 1,500 pounds. The hot air balloon already has 240 pounds of weight in it. If each person that flies in the hot air balloon weighs exactly 180 pounds, how many people can fit in the hot air balloon?

Match the equivalent ratios.

15 miles per hour

miles per hour

per hour

Determine if

A hiker walks at a pace of 2.8 miles per hour. Fill-in the table based on this rate.

Each ticket to the school fair costs $7.25. Fill-in the table based on this rate.

Would the point (1.5, 4.2) fit on the graph of this relationship? Why or why not?

Would the point (5, 36.25) fit on the graph of this relationship? Why or why not?

The graph shows the relationship between the number of soap bottles purchased and the total cost.

The graph shows the relationship between the number of minutes and the number of pages printed.

What is the constant of proportionality?

What would be the cost if 9 bottles were purchased?

What is the constant of proportionality?

How many pages are printed in 7 minutes?

Match the decimals and percents.

Percents to Decimals

Move the decimal two places to the left. 102% → 1.02 0.36% → 0.0036

Decimals to Percents

Move the decimal two places to the right.

0.58 → 58% 0.068 → 6.8%

Use a proportion to find the percent.

Use the percent equation to solve.

= percent • whole a = p • b

is what percent of 90?

= p • 90 p = 0.2 = 20%

Calculate the percent of change.

A jacket originally costs $80. It is on sale for 25% off.

What is the final price of the jacket after the discount?

A restaurant bill is $48. You leave a 20% tip.

How much is the tip, and what is the total bill including the tip?

A store bought a couch for $600 and sold it with a 40% markup. What was the price after the markup?

You deposit $600 in a bank account. After 5 years, you earned $150 in simple interest. What was the interest rate per year?

For each set of shapes, find the scale ratio, scale factor and the missing side.

1. Divide to find the scale ratio and scale factor: 15 ÷ 3 = 5

2. Scale Ratio: 5:1

3. Scale Factor: 1 5

4. Multiply or divide to find the missing side: 25 × 1 5 = 5 m

Scale ratio: Scale factor: x = Scale ratio: Scale factor: x =

Tell whether each set of side lengths can make a triangle. Justify your answer.

9 in, 12 in, 7 in.

1. Add each pair of sides to see if each sum is longer than the third side:

9 + 12 > 7; 9 + 7 > 12; 12 + 7 > 9 Yes, they can make a triangle.

Find the circumference and area of each circle.

radius = 2 m

1. Use 2πr to find the circumference.

2(3.14)(2) = 4(3.14) = 12.56 m

2. Use πr2 to find the area. (3.14)(2)2 = (3.14)4 = 12.56 m2

Circumference = Area = 8. Circumference = Area = 22 m 8 in

Find the circumference and area of each circle.

1. Use angle rules to write an equation.

2x + 104 = 180

2. Solve for the variable. x = 38

3. Substitute the value to find the missing angle measure. 2 × 38 = 76º

An ice cream cone is sliced vertically from top to bottom through the center.

A. What shape is the cross-section?

A paper towel roll is sliced vertically from top to bottom.

A. What shape is the cross-section?

B. If the cone were cut horizontally instead, what shape would the crosssection be?

B. If the roll were cut horizontally instead, what shape would the crosssection be?

A rectangular table is shown below. If the image is scaled by a scale factor of 3 4 , draw the new shape.

Scale the shape below by a scale factor of 7

Find the area of each shape.

1. Substitute values into the area formula. A = 1 2 bh = 1 2 (8)(11)

2. Solve. 1 2 (8)(11) = 44 in2

Find the area of each compound figure. Round to the nearest hundredth if necessary.

1.Identify each shape. 2 rectangles

2. Find the area of each shape. 1: (6)(5) = 30 2: (10)(6) = 60

3. Add the areas of each shape together. 30 + 60 = 90 m2

Find the volume and surface area of each prism. Round to the nearest hundredth if necessary.

1. Substitute values into the correct volume formula and solve. V = Bh = (6)(2)(4) = 48 in3

2. Find the area of each face and add them all up to find the surface area.

S = 2[(6)(2)] + 2[(6)(4)] + 2[(2)(4)] S = 88 in2

A swimming pool has a rectangular section that measures 50 feet long and 20 feet wide. On one end of the pool is a semi-circular diving area with a radius of 15 feet. What is the total area of the pool and diving area combined?

A storage shed has a rectangular base with dimensions 14 feet by 8 feet, and it has a height of 10 feet.

A. What is the volume of the shed?

A sculpture is in the shape of a triangular prism. The base is an equilateral triangle with a side length of 10 inches and a height of 12 inches. The height (length) of the prism is 20 inches.

A. What is the volume of the sculpture?

B. What is the surface area of the shed?

B. What is the surface area of the sculpture?

A rectangular park is 40 feet long and 30 feet wide. Next to the park, there is a circular fountain with a diameter of 20 feet. What is the total area of the park, including the fountain?

Suggest an unbiased sample for each population.

1. People who visit a city park on weekends

2. Books in a school library

Biased Sample Unbiased Sample

3. All students in a middle school

4. Plants growing in a forest

Find the mean, median, and mode.

5. 6, 8, 10, 10, 12

Mean

Sum of the values:

4 + 4 + 6 + 7 + 14 = 35

Divided by total:

35 ÷ 5 = 7 → Average = 7

Median

4, 4, 6, 7, 14

Middle number = 6

Mode

4, 4, 6, 7, 14

Most common number = 4

Find the IQR and range.

1, 2, 2, 7, 8, 10

Mean: Median: Mode: 6. 13, 15, 17, 19, 21

Mean: Median: Mode: 7. 2, 2, 4, 6, 6, 6

Mean: Median: Mode: 8. 9, 11, 13, 15, 17, 19

Interquartile range: Third quartile - First quartile 8 - 2 = 6

Range:

Maximum - minimum 10 - 1 = 9

Mean: Median: Mode:

IQR: Range: IQR: Range:

Calculate the MAD. 11. 1, 3, 5, 7, 9

1, 2, 2, 7, 8, 10

MAD

Mean of the Differences from the Mean (4 + 3 + 3 + 2 + 3 + 5)/6 = 3.3

MAD: 12. 10, 12, 14, 16, 18

MAD: 13. 2, 2, 4, 6, 10

MAD:

A city planner wants to know if residents want a new park. She randomly selects 100 residents from the city’s tax database and mails them a survey.

A. What is the sample?

B. Is this method likely biased or unbiased?

A scientist measures the height (in cm) of a random sample of 5 bean plants grown in sunlight and 5 grown in the shade.

Sunlight: 18, 20, 22, 19, 21 (Mean = 20)

Shade: 10, 12, 14, 11, 13 (Mean = 12)

Based on these samples, what inference can be made about the population of bean plants?

A. Plants in the shade will always grow to exactly 12 cm.

B. There is no difference between the two groups.

C. The typical height of plants in sunlight is likely greater than those the in shade.

D. The typical height of plants in the shade is likely greater than those the in sunlight.

Two bakers are testing new cookie recipes. They bake several batches and count how many chocolate chips end up in 5 random cookies from each batch.

Baker A: 12, 11, 13, 12, 12

Baker B: 8, 15, 6, 18, 10

Which baker is likely more consistent in their baking, as shown by the range?

A veterinarian records the weight (in lbs) of a random sample of Golden Retrievers and Beagles.

Golden Retrievers Mean: 70 lbs

Beagles Mean: 24 lbs

Based on the samples, what inference can be made?

A. Every Golden Retriever weighs 70 lbs.

B. Beagles are generally heavier than Golden Retrievers.

C. The typical weight of Golden Retrievers is likely higher than Beagles.

D. Golden Retrievers weigh 46 more pounds than Beagles.

State the likelihood of each event.

What’s the likelihood of landing on tails when flipping a coin?

0% = impossible

1% – 49% = unlikely

50% = as likely as not

51% – 99% = likely

100% = certain

1. A spinner with 8 equal sections (4 red, 2 blue, 2 green) is spun. What is the likelihood of landing on a red or blue section?

Make predictions using the probability.

A student correctly answers 45 out of 60 questions on practice quizzes. If they complete 200 more questions, how many correct answers should they expect?

1. Determine probability: 3 4

2. Create and solve a proportion.

3 4 = x 200 x = 150

3. A chef prepares 120 meals in a restaurant and receives positive reviews for 90 of them. If the chef serves 400 more meals, how many positive reviews should they expect?

2. You randomly pick a letter from the word "MATH". What is the likelihood of picking the letter M, A, T, or H?

4. A student submits 50 homework assignments, and 42 receive full credit. If they submit 250 more assignments, how many should they expect to receive full credit on?

Answer each question. Write your answers as a fraction, decimal, and percent.

Sally flips a coin 20 times. She lands on tails 12 times.

1. Theoretical = 1 2 = 0.5 = 50%

2. Experimental = 3 5 = 0.6 = 60%

5. A deck of 40 cards is numbered 1 through 40. What is the probability of randomly selecting a card with an even number?

6. A bag contains 12 marbles: 3 red, 4 blue, and 5 green. What is the probability of randomly drawing a blue or green marble?

Organize and answer questions about the sample space using any method.

A clothing store sells 4 types of shirts, 3 pairs of pants, and 10 different hats. How many unique outfits can be created?

1. 4 × 3 × 10 = 120 outfits

7. A car dealership offers 8 car models, each available in 10 colors with 5 different interior options. How many unique car variations are there?

8. A student is designing a custom backpack. They can choose from 5 colors, 3 strap styles, and 4 pocket designs. How many unique backpack designs are possible?

Find the compound probability. Write your answer as a fraction, decimal, and percent.

A coin is flipped, and a six-sided die is rolled. What is the probability of flipping heads and rolling an odd number?

1. Find each probability. P(H) = 1 2 P(odd) = 1 2

2. Multiply: 1 2 × 1 2 = 1 4

9. A person randomly picks a letter from the word "HOMEWORK" and then rolls a standard die. What is the probability of selecting the letter "O" and rolling a 1?

A basketball player has a 3 in 10 chance of making a free throw. Over 200 attempts, the player made 55 shots.

A. What is the theoretical probability of making a free throw?

B. What is the experimental probability of making a free throw?

A vending machine dispenses a randomly selected snack from 5 different options. A study recorded 300 purchases, and one snack was chosen 45 times.

A. What is the theoretical probability of getting any one snack?

B. What is the experimental probability of getting this specific snack?

A trivia contest randomly selects winners from 200 participants, and each person has a 1 in 20 chance of winning. A simulation was conducted, and 7 people won.

A. What is the theoretical probability of winning?

B. What is the experimental probability of winning?

A carnival game has a 1 in 8 chance of winning a small prize. A simulation was conducted where 240 players participated, and 26 won a prize.

A. What is the theoretical probability of winning?

B. What is the experimental probability of winning?

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